WASHINGTON (Reuters) - The heads of the intelligence committees in the Congress said on Sunday an alleged Iranian plot to kill the Saudi ambassador should be taken very seriously, with one warning the United States and Iran could be on a "collision course."

Pushing back against questions about whether the plot was a serious effort endorsed by top Iranian officials, House of Representatives Intelligence Committee Chairman Mike Rogers said it appeared amateurish only because the United States was able to thwart it so early in the planning stages.

"We were very fortunate," Rogers said on ABC's "This Week" program. "We got to see this, we the U.S. government got to see this unfold from the beginning."

Rogers and Senate Intelligence Committee Chairwoman Dianne Feinstein said the United States should respond aggressively but stopped short of calling for military action against Iran, instead pushing for tougher economic sanctions.

Feinstein said she was initially skeptical when she was first briefed about the alleged plot in early September but now believed "it's very real."

Authorities said on Tuesday they had broken up a plan by two men linked to Iran's security agencies to assassinate Saudi Ambassador Adel al-Jubeir in Washington. One of the suspects was arrested last month and the other is at large.

President Barack Obama said on Thursday that Iran -- already at odds with Western governments over its nuclear program -- would face the toughest possible sanctions and the United States would not take any options off the table.

"Our country should not be looking to go to war," Feinstein told the "Fox News Sunday" program. "We should be looking to stop bad behavior, short of war."

Feinstein and Rogers said the United States should push Russia and China to get behind sanctions, arguing the two powers have scuttled past efforts to crack down on Iran over its nuclear ambitions.

"Put pressure on the Chinese and the Russians and say, listen, you're either going to stand with the nation that is engaged in nation-state terrorism or you're going to stand with the rest of the international community," Rogers said.

Feinstein said Iran is "escalating" its nuclear development programs and the assassination plot is one more reason to act now to make clear Tehran must change its policies.

"Absent that at one time or another, if you project out a number of years, we are on a collision course," she said.

(Reporting by Dave Clarke; Editing by John O'Callaghan)