WASHINGTON, Sept 21 (Reuters) - President Barack Obama urged supporters on Saturday to “go back at it” and pursue gun-control measures after mass shootings in Washington and Chicago in the past week put the spotlight back onto the problem of gun violence in the United States.

Obama made passing tough gun laws a top priority after a gunman killed 20 children and six adults at an elementary school in Newtown, Connecticut, in December, stunning the nation.

But Congress rejected his proposals to restrict sales of certain types of guns and require greater background checks. Gun-rights groups opposed the measures, saying they would infringe on Americans’ constitutional rights.

“We fought a good fight earlier this year, but we came up short, and that means we’ve got to get back up and go back at it,” Obama told an awards dinner for the Congressional Black Caucus Foundation.

“As long as there are those who fight to make it as easy as possible for dangerous people to get their hands on guns, then we’ve got to work as hard as possible for the sake of our children ... to do more work to make it harder,” he said to applause.

The Obama administration has largely moved on to other priorities since the gun measures were defeated in Congress, but a recent spate of shootings has brought the issue back into the headlines.

Last Monday, a government contractor killed 12 people during rampage at the Washington Navy Yard before police killed him in a gun battle.

On Thursday night in Chicago, the president’s hometown, suspected gang members opened fire with an assault weapon late at a park, wounding 13 people including a 3-year-old child.

Obama is scheduled to speak at a memorial service for the Navy Yard victims on Sunday and referred to both shootings during his remarks.

However, despite the violence and Obama’s remarks, the political appetite for gun control on Capitol Hill has not changed, and a broad new effort by the administration is unlikely as it works on immigration reform and budget battles that threaten to shut down the government.

The Republican-controlled House of Representatives passed a bill on Friday to fund the government, but only if Obama’s landmark healthcare law - which is detested by his political opponents - is ransacked.

Obama lashed out at Republicans for that and reiterated his pledge not to negotiate whether to raise the U.S. debt ceiling, which is necessary for Washington to pay its bills.

“This is an interesting thing to ponder, that your top agenda is making sure 20 million people don’t have health insurance, and you’d be willing to shut down the government and potentially default for the first time in United States history because it bothers you so much,” he said.

“Let me say as clearly as I can: It is not going to happen ... We will not negotiate over whether or not America should keep its word and meet its obligations. We’re not going to allow anyone to inflict economic pain on millions of our own people just to make an ideological point.”