By Richard Cowan and David Morgan

WASHINGTON (Reuters) - The U.S. Congress is headed for a seven-week recess without addressing gun violence, the Zika virus outbreak and other pressing issues, amid persistent election-year bickering.

Despite recent gun violence, the House of Representatives will not vote this week on a proposal to keep firearms out of the hands of people on terrorism watch lists, that chamber's Republican leader Kevin McCarthy told reporters on Tuesday.

Similarly, President Barack Obama's request for $1.9 billion in funds to combat the Zika virus and the birth defects it can cause has been stalled in Congress since February.

Republicans and Democrats were also at odds over spending bills to keep the government functioning beyond Sept. 30, when current fiscal year funding expires.

When Republicans took control of Congress, they vowed to get things done but have had difficulty doing so during this election year, failing to pass a budget or even consider Obama's nomination of Merrick Garland to fill a Supreme Court vacancy.

Congress did, however, approve bipartisan legislation helping Puerto Rico out of a crippling debt crisis and is trying to make progress on legislation to improve police relations with local communities in the aftermath of gun violence.

With barely four days left before the start of an unusually long recess, a failure to vote on guns would postpone any possible action by the House until at least Sept. 6, when lawmakers return.

After that, they will work only for short stints ahead of the Nov. 8 presidential and congressional elections.

Mass shootings in Orlando and Dallas, and gun violence in other cities, has again propelled gun control to prominence. But the National Rifle Association and its allies in Congress so far have staved off legislation.

Gun control is generally opposed by Republicans and supported by Democrats. Some Republicans have talked about a gun bill possibly moving through Congress in the fall, in the midst of the campaign season, but Democrats were skeptical.

"This Congress will do nothing on curbing gun violence," Representative Xavier Becerra of California, a member of the House Democratic leadership, told reporters.

The two sides even disagree on whether House Speaker Paul Ryan and House Democratic leader Nancy Pelosi talked about a proposal to establish a special committee to study gun violence. Democrats say Pelosi raised the issue with Ryan last week. Ryan's office says he has never discussed the topic with anyone.

Republicans in the House and Senate have signed onto a $1.1 billion Zika funding bill. But Democrats are balking over what they see as "poison pills" attached to the money that would deny funds to women's healthcare provider Planned Parenthood and ease some environmental provisions.

Democrats, who warn the current legislation will not pass the Senate, said on Tuesday that they offered to accept some Republican provisions. But Senate Republicans insist the bill cannot be altered.

Ryan meanwhile showcased his "A Better Way" agenda, flashing a glossy pamphlet at a press conference listing proposals designed to lure votes in November but do nothing this year legislatively.

Republicans have also pushed for new federal probes of Hillary Clinton, the presumptive Democratic presidential nominee, on her use of private emails while secretary of state.

(Reporting by Richard Cowan, David Morgan and Kouichi Shirayanagi; Writing by Mohammad Zargham; Editing by Kevin Drawbaugh and James Dalgleish)