Theresa May will face pressure from the defence secretary to publish an interim report on the government’s defence review before the Nato summit later this month to demonstrate to international allies her commitment to the armed forces.

Gavin Williamson is expected to attend talks with the prime minister and the chancellor at Downing Street next week where the Guardian understands he will make one final push for her to sign off his modernising defence review.

Whitehall sources said Williamson felt the Nato summit in Brussels later this month presented the government with a unique opportunity to boost Britain’s global influence by showcasing its plans to leaders including the US president, Donald Trump.

The defence secretary faces an uphill battle as No 10 sources indicated May was unlikely to agree to interim publication as she had already told Williamson that his first draft of the plan was not fit for the future and needed more work.

One source said: “It was half-baked. Publishing even a bit of it just now to show our strength at Nato would be problematic.”

The review is aimed at shaking up British defence and security capability to match 21st-century threats. May believes it must protect the UK against cyber-attacks and other new threats, with a reduced focus on more traditional military hardware.

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However, the prime minister has twice shied away from pledging that the UK should remain a “tier one” military power on par with the US, Russia, China and France, even though the phrase is understood to feature in the review. She was said to have asked Williamson to explain what that would mean for UK in practice.

Ministry of Defence officials are concerned that the focus on new threats should not come at the expense of the UK being ready to respond to “conventional” ones. “It’s not about either/or, it’s about having a complementary set of capabilities,” said one.

There has been an increasingly acrimonious relationship between Williamson and the chancellor, Philip Hammond, over a push for an extra £2bn a year in defence spending on top of the existing £35.3bn budget. The defence secretary’s intense politicking is understood to have irritated both No11 and No10.

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Whitehall sources played down reports that next week’s meeting would be used by Williamson to push for more money for defence, adding that finances were only expected to come up in the context of the MoD becoming more efficient.

One said: “The MoD got £800m extra at the end of March and that’s given relief for this year. We wanted to do something in and around the Nato summit so we can unveil headline conclusions from the defence review and make a statement of intent on our capability, as opposed to showing how much we are spending.”

Ministers are concerned about Trump’s plan to meet Vladimir Putin on 16 July in Helsinki, straight after the Nato summit and his visit to the UK. It will put May under pressure to use the visit to convince him not to do any sort of deal with Russia that may harm Nato or heighten tension on Europe’s eastern borders.