The president of Yemen secretly offered US forces unrestricted access to his territory to conduct unilateral strikes against al-Qaida terrorist targets, the leaked US embassy cables reveal.

In a move that risked outraging local and Arab opinion, Ali Abdullah Saleh told Barack Obama's deputy national security adviser, John Brennan, in September 2009: "I have given you an open door on terrorism. so I am not responsible," according to a secret dispatch back to Washington

In reality, despite the offer of an "open door", Yemen has restricted access for US forces in order to avoid playing into the hands of Saleh's domestic critics.

The cables expose for the first time the true scale of America's covert military involvement in the Arab world's poorest nation amid deep concern in Washington that it has become the haven for al-Qaida in the Arabian Peninsula (Aqap).

The group has carried out a series of attacks on western targets, including the failed airline cargo bomb plot in October and the attempt to bring down a US passenger jet over Detroit on Christmas Day last year.

While Saleh's government publicly insists its own forces are responsible for counter-terrorism operations, the cables detail how the president struck a secret deal to allow the US to carry out cruise missile attacks on Aqap targets. The first strike in December last year, which killed dozens of civilians along with wanted jihadis, was presented by Saleh as Yemen's own work, supported by US intelligence.

But a cable dated 21 December from the ambassador Stephen Seche recorded that "Yemen insisted it must 'maintain the status quo' regarding the official denial of US involvement. Saleh wanted operations to continue 'non-stop until we eradicate this disease.'" A second attack took place on 24 December.

A few days later, in a meeting with General David Petraeus, then head of US central command, Saleh admitted lying to his population about the strikes.

"We'll continue saying the bombs are ours, not yours," Saleh told Petraeus on 2 January. That prompted the deputy prime minister, Rashad al-Alimi, who was also at the meeting, to joke he had just "lied" by telling parliament the bombs in Arhab, Abyan, and Shebwa (the al-Qaida strongholds) were American-made but deployed by Yemen.

Petraeus had flown to Sana'a to tell Saleh that Barack Obama would allow US ground forces "armed with direct-feed intelligence" from satellites or surveillance aircraft to be deployed in Yemen on counter-terrorist operations. But in contrast to his suggestion of an " open door", Saleh rejected the offer, expressing concerns about US casualties.

Instead it was agreed to have "US fixed-wing bombers circle out of sight outside Yemeni territory ready to engage Aqap targets should actionable intelligence become available". US personnel would have to stay in the Yemeni command centre.

Saleh said "mistakes had been made" in the earlier strikes, lamented the use of US cruise missiles that were "not very accurate" and welcomed the use of aircraft-deployed, precision-guided bombs instead.

Petraeus told Saleh he had requested $150m (£95m) in security assistance for Yemen for 2010, a substantial increase over the 2009 amount of $67m. Later in 2010, discussions were reported on raising US security assistance to Yemen to more than $1bn.

The US air strikes were praised by Saudi Arabia, the cables show. The deputy interior minister, Prince Mohammed bin Nayef, told General James Jones, Obama's national security adviser: "The Saudis have been monitoring conversations of al-Qaida operatives in Yemen very closely and whereas before the attack they were hearing relaxed 20-minute phone conversations over cellphones, after the attack the phones went virtually silent. This suggests that at least for now these operatives are more focused on their own security rather than on planning operations."

Bin Nayef's support for operations against Aqap is perhaps unsurprising. He survived an assassination attempt in Jeddah in September 2009 when a Saudi Aqap operative named Abdullah al-Asiri feigned repentance for his jihadi views in a meeting with the prince then blew himself up with a bomb concealed in his anus.

The secret dispatches also detail how Yemen repeatedly failed to implement anti-terror training for airport officials, allowed cargo to pass through x-ray machines unchecked and refused to co-operate over American suspicions about the movement of students through Islamic institutions.

On 31 January 2010 America's most senior counter-terrorism official warned the Yemeni president of the need for tougher airport security after the US embassy reported that security advice had gone unheeded for more than a decade.

In a face-to-face meeting with Saleh, Daniel Benjamin "reiterated the US government's desire to ensure that no international terrorist attack originates again from Yemen", according to a cable from the embassy in Sana'a. He urged Saleh to accept fresh US help to "strengthen screening procedures at all of Yemen's international airports".

The meeting took place in the aftermath of the failed Christmas Day terror attack on a Northwest Airlines plane over Detroit. The Nigerian "underpants bomber" Umar Farouk Abdulmutallab, who tried to blow up the flight from Amsterdam, was radicalised in Yemen while claiming to be there as a student.

Ibrahim Hassan al-Asiri, a Saudi-born militant active in Yemen, is alleged to have been responsible for making that bomb and is also suspected of building the computer printer bombs found on flights from Sana'a, destined for Chicago, one of them in transit in the UK. Aqap claimed responsibility for both plots.

The US cables reveal that Yemen balked at the state department's request to share information about student's movement in and out of the country, despite intelligence to suggest some of its universities and madrasas play a key role in al-Qaida recruitment.

Benjamin told Saleh the US wanted to "establish a mechanism for sharing information on passengers travelling via air to and from Yemen as well as foreign nationals who have come to Yemen to study at language or religious institutions". But Yemen's security committee said the request was "too broad".

At times the relationship between the US and the Yemeni president appears strained. Saleh said he was satisfied with America's counter-terrorism assistance to date, but "appealed for the acceleration of additional support, citing helicopters and vehicles with IED-jamming devices". He described the Americans as "hot-blooded and hasty when you need us", but "cold-blooded and British when we need you".

In 2009 Seche reported airport security in Yemen was poor and US anti-terror training for airport officials and security staff offered since 1998 had not been effectively implemented. "There have been numerous occurrences of x-ray screeners not watching their monitors constantly, and ineffective access control procedures," he said.

Customs officials were ineffective, "underpaid, poorly trained and receptive to corruption," he said. A tour of the airport by a US security delegation in June 2009 revealed "several lapses in airport security practices … regarding passenger screening, cargo security, and secure identification display area badge and access procedures".

The cables reveal how the US saw Yemen's ability to fight al-Qaida on the ground as weak despite the country's emergence as the next most important front in the fight against the group. Until January 2010, its main counter-terrorism control centre was equipped with only three computers, counter-terrorist officers on the ground only communicated sporadically using mobile phones which often failed, and the only mapping available was paper charts, Seche told Washington.

Recent Yemeni counter-terror operations had been "impeded by a lack of clear commands, miscommunication between counter-terrorism elements regarding roles, information that was not shared until after the operation, and a reliance on sporadic cellphone calls between various units in the field during the course of the operation". Seche quoted Yemen's counter-terrorism unit commander, Kamal al-Sayani, admitting that "almost 80% of relevant information never makes it to the tactical counter-terrorism unit leaders in the field".

US officials expressed concern that close support for Saleh could backfire: "While Yemeni counter-terrorism activity and co-operation have been strong in recent months," Arab allies were told on the eve of a London conference on aid to Yemen, "we are concerned that Saleh's willingness to target Aqap will wane if domestic opposition paints Saleh as a pawn of the United States for these actions. Public Arab support to Yemen's counter-terrorism activities may help Saleh weather internal criticisms in this regard".

Diplomats were privately sceptical about Yemeni determination. "To the extent that our public statements continue to reflect a sensitivity to the 'amour-propre' of Yemen's leadership on this subject, we can expect the Yemeni government to continue to publicly affirm its seriousness about prosecuting its counter-terrorism objectives and perhaps to match these expressions of intent with actions on the ground," the ambassador said.