Keir Starmer has insisted he can maintain a “good relationship” with Donald Trump after the Republican candidate’s campaign accused Labour of “blatant foreign interference” in the US election.

The Trump campaign filed a legal complaint overnight against Labour officials travelling to US battleground states to volunteer for his Democrat rival Kamala Harris.

The letter, which was sent to the US Federal Election Commission, said that these volunteering efforts and reports of contact between Labour and the Harris campaign amounted to “illegal foreign national contributions”.

A statement on DonaldJTrump.com on Tuesday night claimed that the “far-left” Labour party has “inspired Kamala’s dangerously liberal policies and rhetoric”.

In response Starmer insisted he had a “good relationship” with Trump which would not be jeopardised by the complaint.

The prime minister said that party officials volunteering for Harris ahead of the US presidential election on 5 November were “doing it in their spare time” rather than in their capacity working for Labour.

Speaking to reporters travelling with him to the Commonwealth summit in Samoa, Starmer said: “The Labour party … volunteers, have gone over pretty much every election. They’re doing it in their spare time, they’re doing it as volunteers, they’re staying I think with other volunteers over there.

“That’s what they’ve done in previous elections, that’s what they’re doing in this election and that’s really straightforward.”

Asked if the complaint risked jeopardising his relationship with Trump if he becomes president again, the prime minister said: “No. I spent time in New York with President Trump, had dinner with him and my purpose in doing that was to make sure that between the two of us we established a good relationship, which we did, and we’re grateful for him for making the time.”

“We had a good, constructive discussion and, of course as prime minister of the United Kingdom I will work with whoever the American people return as their president in their elections which are very close now.”

The complaint cited a now-deleted LinkedIn post by Labour’s head of operations, which said almost 100 current and former party officials were travelling to the US to campaign for the Democrats in swing states including North Carolina, Nevada, Pennsylvania and Virginia. The post added that there were 10 spots still available and promised that “we will sort your housing”.

The letter, sent by Trump campaign lawyer Gary Lawkowski, mentioned newspaper reports of contact between senior Labour advisers and the Harris campaign and called for an immediate investigation.

It drew a comparison to a programme in 2016 in which the Australian Labor party (ALP) sent delegates to help Bernie Sanders’ campaign. In that instance the US Federal Election Commission fined the ALP, which paid for its delegates’ flights and gave them daily stipends, and the Sanders campaign $14,500 each.

Labour has said that activists’ trips are not organised or funded by the party and that any officials who campaign in the US election are volunteers who do so in their own time.

Starmer met Trump during a trip to New York in September and visited Trump Tower for talks ahead of the US election. Trump heaped praise on Starmer ahead of their meeting, saying he was a “very nice” man who “ran a great race” in the UK election and was “very popular”.

The Trump campaign’s complaint said: “When representatives of the British government previously sought to go door-to-door in America, it did not end well for them. This past week marked the 243 anniversary of the surrender of British forces at the Battle of Yorktown, a military victory that ensured that the United States would be politically independent of Great Britian [sic].”

“It appears that the Labour party and the Harris for President campaign have forgotten the message.”