WASHINGTON — Congress doesn’t have any evidence so far of a White House coverup involving a botched gun-tracking operation, a top Republican said Sunday, countering the House speaker’s assertion that President Obama or his aides deliberately misled lawmakers.

‘‘No we don’t,’’ said Representative Darrell Issa of California in response to a question on ‘‘Fox News Sunday’’ about whether lawmakers had proof now to back Speaker John Boehner’s claim about White House officials’ involvement.

‘‘And I hope they don’t get involved. I hope this stays at Justice,’’ said Issa, chairman of the House Oversight and Government Reform Committee.

The Republican-led committee voted along party lines Wednesday to cite Attorney General Eric Holder for contempt of Congress for not handing over all the material demanded in Operation Fast and Furious. Earlier that day, Obama had invoked executive privilege to withhold the documents, which concern how the department learned there were problems with an Arizona probe of gun-running into Mexico.

Boehner, an Ohio Republican, has said the full House would vote on the matter this coming week unless there was some resolution in the meantime. He also said that Obama’s claim of executive privilege was ‘‘an admission the White House officials were involved in the decision that misled the Congress and covered up the truth.’’

But Issa said Sunday that he didn’t have any evidence yet that Obama or White House aides were involved, and he made clear that his inquiry has focused, for now, on the Justice Department.

The committee’s top Democrat, Representative Elijah Cummings of Maryland, said he thought the two sides could reach an agreement before the House vote and he called on Boehner to ‘‘come forth and show strong leadership’’ by sitting down with Holder.