He noted that the USA assassinated Soleimani because he foiled Washington's plots against the regional people.
Democrat Congress member Ro Khanna, responded by suggesting that Soleimani was killed in revenge for his responsibility in the death of Americans.
Democrats and a few Republicans in Congress said they have not been given adequate, detailed briefings.
Nine Senate Democrats on Tuesday demanded a new classified briefing from the nation's top intelligence official seeking specific evidence underlying Trump statements that Iran was planning imminent attacks on four USA embassies.
While Mr Esper said he agreed with Mr Trump that additional attacks against U.S. embassies were likely, he said on CBS's Face the Nation that Mr Trump's remarks to Fox News were not based on specific evidence of attacks on four embassies.
"And I think we can achieve both of these goals - reduce our footprint, reduce our risk, while still achieving the American objectives in the region, including in Iraq", he said. While President Donald Trump has often talked about bringing troops back home, his administration has so far shown no signs of permanently ceasing operations in Iraq, Syria or elsewhere in the Middle East. "My guess is that the details don't exist".
The killing marked a significant escalation between Iran and the United States, and angered Iraq's Shi'ite majority, which has religious ties with Iran. Perhaps the reluctance to share the information is because there is nothing there that shows there was any imminent attack on United States embassies or on any other facilities.
Separately, a senior State Department official told Fox News, "We still have concerns about Iranian proxy groups in the region".
Two of Trump's most prominent Cabinet officials echoed that message on Monday.
"Our ability to deter attacks had obviously broken down", Barr said. U.S. officials may be changing there stories so as not to appear to be contradicting President Trump as they fear that contradicting him could very well have negative consequences for their careers.
Trump himself implicitly acknowledged the deterrence aim, telling reporters Monday that the strike against Soleimani "should have been done 20 years ago".
When Fox News anchor Bret Baier asked Pompeo whether the Trump administration described the threat to the four embassies as "imminent" because "it pleased the lawyers", Pompeo said he was unsure "who used it first, but it reflects what we saw".
"The answer to both is a strong YES., but it doesn't really matter because of his awful past!"
Rouhani also said that the U.S.is seeking to gain control over oil wells in Syria. He said Major-Gen Soleimani was a "legitimate military target" and the strike was a "legitimate act of self-defence".
In March 2019, supreme leader Ayatollah Ali Khameini presented Soleimani with the Order of Zulfiqar, Iran's highest military honor, as a champion of the Islamic revolution of 1979 and defender of the nation at home and overseas.
Soleimani had been in the cross-hairs of the US before - at least once in 2007 - but two administrations had rejected operations to kill him, wary of the consequences of striking down the Iranian military leader.
Around this same time, Russian Federation joined Iran in backing the Syrian government, which has retaken most of the country.
Syrian Prime Minister Emad Khamis met Tuesday with Iranian President Hassan Rouhani in Tehran, and called for an end to US troops operating in the country for years without the government's permission, adding that other regional powers should also step up in calling for USA military withdrawals.