Senior Tory MPs have rallied behind Boris Johnson, saying that he and Theresa May were an ideal double act who should use their “chalk and cheese” personalities to deliver a successful Brexit and redefine the UK’s position on the world stage.

Amid fears in Whitehall that the relationship between the prime minister and foreign secretary – and their two offices – is close to breaking point, Brexit supporters are determined to protect Johnson in the face of criticism and a series of slapdowns from No 10.

Allies of Johnson told the Observer that the foreign secretary “is going nowhere” and that May will have to sack him if she continues to be irritated by his public statements and wants him out of the Foreign Office.

Friends of Johnson at Westminster also made clear that they had relayed their displeasure to No 10 over the way Johnson had been so publicly criticised by Downing Street last week after he accused Saudia Arabia of acting as a “puppeteer” in “proxy wars across the Middle East” at a meeting in Rome.

“That point has certainly been made,” said one friend. “It could have been sorted out with a few phone calls rather than with comments to the media which are then presented as a huge slapdown. We have to avoid that in future.”

Meanwhile, MPs tried to play down the tensions, insisting that a minor issue had been blown out of proportion in the press and that May and Johnson would be an effective partnership at a crucial time for the UK with Brexit and the Donald Trump presidency presenting huge challenges.

Crispin Blunt, Tory chair of the all-party foreign affairs select committee, said that their different qualities could be a great asset: “The country needs Boris’s imagination and sense of historic perspective alongside the prime minister’s discipline, including in overseeing negotiations on our exit from the EU. They have complementary skill sets which we need.”

Bernard Jenkin, Tory chair of the public administration select committee, insisted that nothing Johnson had said or done had damaged the unity of the government or harmed international relations.

“His free thinking is a useful counterpoint to the more delphic approach of the prime minister,” Jenkin said. “I am sure they will work together very well in future.”

Another senior Tory MP, who backed Johnson for the leadership before he withdrew from the race in July, said: “Theresa May knows she and Boris are chalk and cheese personalities. We have to see that as an asset, not a problem.”

On a visit to meet Arab leaders on Friday evening Johnson made no mention of his comments about Saudi Arabia in Italy the previous week, when he accused the UK’s closest ally in the region, Saudi Arabia, of “puppeteering and playing proxy wars”.

He told Arab leaders in Bahrain: “I of course understand Saudi concerns about security and the paramount importance of Saudi Arabia securing itself from bombardment by the Houthis” – a reference to the former rebel movement that now controls parts of Yemen including the capital, Sana’a.

He added: “But I must also share my profound concerns, which I’m sure is universal in this room, about the present suffering of the people of Yemen.

“I think we can all agree on this key point, that force alone will not bring about a stable Yemen, and that’s why we in London have been working so hard with all our partners to drive that political process forwards.”

On Saturday he joined US secretary of state John Kerry and other international leaders for talks on the humanitarian situation in Aleppo and across Syria, and efforts to renew the political process to find a solution to the conflict.

Following the meeting, Johnson said: “The situation in Aleppo remains dire with desperate images of destruction and a flagrant disregard for human life being splashed across the media on a daily basis.

“We agreed our first priority must be the protection of civilians and ensuring access for humanitarian aid. It’s essential that the regime and its backers provide the United Nations that access with immediate effect.”