An influential Conservative think tank has urged Boris Johnson not to shy away from tackling human rights concerns following the foreign secretary's visit to Saudi Arabia, days after he had criticised Riyadh for stoking "proxy wars" across the region.

Both countries played down comments by Johnson that Saudi Arabia was guilty of "twisting" Islam and "puppeteering".

In a press conference with his Saudi counterpart on Sunday (11 December), Johnson appeared to soften his stance, expressing "deep concern" for the humanitarian situation in Yemen, where a Saudi-led coalition is accused of rights abuses.

He also said he wanted to "emphasise the friendship" between the countries, adding: "And it's also fair to say that we believe in candour in our relationship. Now is the time for us to talk about the positive things that we are doing together."

It is understood his comments about "puppeteering" were not raised in any of his meetings in Riyadh.

But the Bright Blue think tank, which has about 130 Tory MPs and peers among its supporters, said it was right for Johnson to have raised human rights concerns.

Dominic Grieve, the former attorney general who is part of the commission, told The Guardian: "Encouraging a debate on how we promote human rights as part of foreign policy is completely sensible.

"Many people might find the foreign secretary's comments quite reassuring in some ways, that he takes human rights issues seriously. I certainly don't want to be castigating the government for doing what is a difficult job. But I do think you need to keep the issue in mind."

Ryan Shorthouse, director, of Bright Blue, which has set up a commission to look at the links between human rights and government policy, said Johnson should not be warned away from discussing human rights. He said: "It is important that the foreign secretary speaks out more on these issues and is better advised and held to account on doing so."

Saudi foreign minister Adel Jubeir said Johnson's comments about "proxy wars" had been taken out of context by the media and the matter was now closed.

A Foreign Office spokesman said the meeting between Johnson and King Salman had been "warm and genial", adding: "They covered a broad sweep of history of UK-Saudi relations and shared interests in the region," the BBC reported.

But the Labour Party are questioning whether the Conservatives should proceed with plans to downgrade parliamentary scrutiny of UK arms exports licences, including to Saudi Arabia.