The U.S. House of Representatives has passed "Kate's Law," a bill inspired by the 2015 shooting death of Pleasanton native Kathryn "Kate" Steinle on a San Francisco pier by an oft-deported undocumented immigrant with a history of criminal convictions.

Formally House Resolution 3004, Kate's Law would increase punishments for criminal offenders who re-enter the country illegally after deportation. The legislation now heads to the Senate for consideration, and President Donald Trump has indicated support for the bill if presented to him for approval.

Pleasanton's Congressman Eric Swalwell was among the two-dozen Democrats who voted in favor of Republican-sponsored Kate's Law on Thursday afternoon in Washington, D.C.

In a statement, Swalwell said Steinle's killing nearly two years ago touched him personally, and though the proposed legislation named for her could have been improved, it provided an opportunity to strengthen enforcement against repeat offenders.

"I knew Kate Steinle growing up and remain in touch with her family, who live in my congressional district," the Dublin Democrat said. "Her heinous murder was a tragedy and we still grieve today, wishing she was still with us. Sadly, we can't bring Kate back, but lawmakers can work to try and better protect our communities from criminals hurting people."

"This bill is not perfect, and it's shameful that the Republicans did not allow any debate in the Judiciary Committee, on which I sit, or on the House Floor to improve it. But it does improve our ability to punish individuals who repeatedly break the law and to deter those who may do so," added Swalwell, a former Alameda County prosecutor.

In another key immigration vote Thursday, the House passed the "No Sanctuary for Criminals Act," which cuts off some federal funding for so-called sanctuary cities. Swalwell opposed that bill, House Resolution 3003, in the nearly party-line vote.

Steinle's shooting death -- and Republican legislation introduced in the wake of it -- has captured national headlines and spurred new debate on immigration enforcement and sanctuary city policies since that fateful evening on Pier 14 on July 1, 2015.

An Amador Valley High alumna living in San Francisco at the time, 32-year-old Steinle was walking with her father on the pier when she was shot and killed. Authorities later arrested and charged Juan Francisco Lopez-Sanchez, an undocumented Mexican immigrant who had been deported five times and had seven convictions.

Investigators said Lopez-Sanchez was in San Francisco Sheriff's Office custody weeks earlier, but was released when his drug-related charges were dismissed. Immigration officials weren't notified because of San Francisco's "sanctuary city" policy, which means local law enforcement does not hold people for immigration violations alone.

The investigation later revealed the gun used to kill Steinle had been stolen from a U.S. Bureau of Land Management ranger's vehicle where it had been left unsecured, and the bullet that struck the Pleasanton native actually ricocheted off the ground before hitting her in the back.

The criminal case against Lopez-Sanchez is ongoing. He has pleaded not guilty to second-degree murder for Steinle's death, with his defense attorney arguing the gun fired accidentally after he allegedly found it wrapped in a T-shirt.

Pending too is legislation inspired by Steinle's slaying, but Kate's Law got a big boost Thursday afternoon, two days before the second anniversary of her death.

HR 3004, introduced by U.S. Rep. Bob Goodlatte (R-Va.) earlier this month with 16 Republican cosponsors, would amend the Immigration and Nationality Act to create new punishments for immigrants re-entering the U.S. after deportation.

It differs from a previous version of Kate's Law, which failed to advance in Congress, that proposed to increase the maximum prison sentence to five years -- up from two -- for immigrants who repeatedly try to enter the country illegally, among its other provisions.

The current Kate's Law proposal focuses on penalties for deported criminal offenders, like Lopez-Sanchez, who repeatedly try to get back into the U.S. after deportation.

It specifically applies to "any alien who has been denied admission, excluded, deported, or removed, or who has departed the United States while an order of exclusion, deportation, or removal is outstanding, and subsequently enters, attempts to enter, crosses the border to, attempts to cross the border to, or is at any time found in the United States."

For those criminal immigrants with three or more misdemeanor convictions or a felony conviction, they could be imprisoned up to 10 years if caught re-entering the country.

If they had served 30 months or more for their felony conviction, they could imprisoned up to 15 years for the new immigration violation; if 60 months or more was served, then the new prison sentence could be up to 20 years; and if they were previously convicted of murder, rape, kidnapping or another serious felony, then the new punishment would be up to 25 years.

HR 3004 would also create a new maximum prison sentence of 10 years for an immigrant caught illegally entering the country after three or more previous deportations.

The House passed this version of Kate's Law 257-167, mostly on party lines with 24 Democrats in favor, including Swalwell.

After the vote Thursday afternoon, President Trump tweeted that he hoped the Senate would soon follow suit and pass "Kate's Law." Trump offered strong support for the bill the day before.

"H.R. 3004 would increase the penalties that may be imposed on criminal aliens convicted of illegal reentry, deterring reentry and keeping criminal aliens off our streets. The bill is consistent with the administration's broader efforts to strengthen enforcement of our immigration laws and improve the security of our nation's borders," the White House said in a statement Wednesday.

Trump has also voiced support for HR 3003, better known as the No Sanctuary for Criminals Act. Also introduced by Goodlatte, with 14 Republican cosponsors, the bill passed the House 228-195 on Thursday.