Senior Republicans in Congress have written to Hillary Clinton, the US secretary of state, claiming to have evidence of a previously undisclosed attack on the US consulate in Benghazi and threats to American ambassador in Libya in the months before he was killed.

Darrell Issa, chairman of the House oversight and government reform committee, and Jason Chaffetz, chairman of a subcommittee on national security, are demanding Clinton hand over information about previous attacks and threats as Republicans step up pressure on the White House with accusations of incompetence and a cover-up over the assault that killed the US ambassador, Chris Stevens, and three other American officials last month.

The letter says that US diplomats in Libya made repeated requests for increased security at the Benghazi consulate but were rejected by officials in Washington. The congressmen have called a hearing for October 10 and want Clinton to reveal what the state department knew about earlier incidents and how it responded to the growing security threat.

Issa and Chaffetz have disclosed an attack on the US consulate on April 6 in which two Libyan former guards at the building who had been fired threw a homemade bomb over the fence. No one was hurt. That incident came two months before a bomb blew a large hole in the consulate gates, again without causing casualties. The second attack was already public knowledge.

Issa and Chaffetz say that whistleblowers also pointed to other incidents that should have caused the US administration to better protect its diplomats in Benghazi. These include threats made openly on Facebook.

An attack on the International Red Cross compound in May was followed by a claim of responsibility on Facebook which said it was a "message for the Americans disturbing the skies over Derna" – taken to mean US drones flying over a Libyan city that was a recruiting ground for anti-US insurgents in Iraq.

The letter says that the following month a Facebook page linked to supporters of the dead Libyan dictator, Muammar Gaddafi, directly threatened Stevens and included a reference to his jogging route. Issa and Chaffetz say that "after stopping these morning runs for about a week, the ambassador resumed them."

Issa and Chaffetz also say that weeks before the assault that killed Stevens' and three other officials, Libyan guards at the consulate employed by a British company, Blue Mountain Group, were warned by family members to resign because of rumours of a looming attack.

The New York Times on Monday reported that some American officials believe that the relatively small scale and swift response by Libyan security guards to the earlier incidents may have led to a false sense of security.

Republicans accuse the Obama administration of misreading the warning signs in the run-up to the full scale attack on the Benghazi consulate on September 11, and then of covering up the true nature of what they say was a well-planned terrorist assault with links to al-Qaida.

Senior Democrats accuse Republicans of playing politics with Stevens' death.

The administration has rejected a call from congressman Peter King, chairman of the House homeland security committee, for Susan Rice, the US ambassador to the UN, to resign after she presented the White House's initial claim that the attack was spontaneous and a reaction to a short anti-Muslim video on You Tube that prompted protests across the Middle East.

Issa and Chaffetz say the evidence in their letter demonstrates that the assault on the Benghazi consulate was well planned.

"It was clearly never, as administration officials once insisted, the result of a popular protest," the letter said.

King echoed the criticism and accused the Obama administration of an intelligence failure in not reading the warning signs and giving sufficient protection to the consulate and Stevens.

"Why did the administration ignore these warning signals over the last few months? We had attacks on our own consulate, we had attacks on the British ambassador, we had attacks on the Red Cross," he told Fox News on Tuesday. "It's such a dangerous area and yet nothing was done as far as securing the compound there. The ambassador was travelling with minimal security. And then when the event did occur, the administration went on for more than a week, two weeks, denying it was a terrorist attack."

Republicans accuse the administration of shifting position after it acknowledged on Friday that there was a "deliberate and organised terrorist attack". However, there remains a strong difference of opinion over what that means.

Republicans are choosing to equate "terrorist attack" with al-Qaida. A steady stream of members of Congress have appeared on Fox News to suggest that a Libyan militia could not have launched such a comprehensive and well-armed assault without outside help. Some critics point to the precision of mortar attacks during the assault which suggest well trained fighters, although they could have served in Gaddafi's army.

Administration officials point out that there are several militias in Benghazi armed with weapons seized from Gaddafi's military during last year's revolution, which could have launched the assault on their own initiative.

King accused the administration of a cover-up. "It fits into the president's narrative that there's not really a threat from al-Qaeda, there's just a threat from a few radicals out there who get excited about a video," he told Fox News.

"The Obama administration has a view of the world and, whether they do it intentionally or not, they end up selectively putting in facts that fit into their narrative. The president's narrative is that al-Qaida has been decimated and the war against terrorism has been won, and now we can turn our attention to the Pacific."

Another member of Congress, Marsha Blackburn, went so far as to compare the alleged cover-up with Watergate.

"This is why we need an independent counsel and we need the investigations top begin immediately," she told Fox News. "Benghazi-gate is the right term for this. This is very, very serious; probably more serious than Watergate."

Sorting the claims and counter-claims has been made more complicated by the failure of FBI investigators to visit Benghazi because of fears for their security.

The Libyan government on Tuesday said plans are finally being made for FBI agents to travel to the city but that details of the cooperation agreement between the US and Libya on the investigation have still to be finalised.

The state department said on Monday that it has now pulled all US officials out of the city and closed the consulate there.

"Everybody who was in Benghazi and posted there has been withdrawn," said the state department spokeswoman, Victoria Nuland. The US embassy in the Libyan capital, Tripoli, remains open with reduced staffing.