The Northern Ireland Secretary has been criticised for his "unhelpful intervention" over the DUP leader's decision not to become First Minister.
Brandon Lewis suggested to the Sunday Times that it would be a mistake and make things more difficult if Edwin Poots did not take on the top role.
The new DUP leader said he will nominate a colleague as First Minister, stating that he wants to focus on the party.
Mr Poots is set to announce his ministerial team by the end of the week.
The DUP's Paul Givan is widely tipped to take on the role of First Minister after Arlene Foster steps down.
Mr Lewis told the newspaper that Mr Poots would not have regular access to the Secretary of State or Prime Minister Boris Johnson.
"When we have meetings with the devolved authorities and the Prime Minister it is with the First Minister and deputy First Minister, it's not with the party leaders," Mr Lewis said.
"When there's a royal visit, it's with the first and deputy first minister.
"Having the leader of the largest party which has the first minister not be the first minister will make things more difficult."
However, Alliance leader Naomi Long said the intervention by Mr Lewis was not "helpful".
Ms Long also said Mr Givan would not be her first choice as she is "not a fan" of the DUP.
"Paul and I have worked together on the committee, we've managed our relationship as reasonably well as we can, given our differences of view," Ms Long told the BBC.
"The matter of who is going to be First Minister is a matter for Edwin Poots and I am not going to interfere in the internal politics of the DUP.
"It's for Edwin to choose the person that he believes is best placed to represent his party in that role, and it's my job as leader of the Alliance Party and Justice Minister, to work to the best of my ability with whoever he puts into that role."
Mr Lewis also suggested to the paper that he was "running out of patience" with the Executive's failure to deal with Irish language and abortion services.
In the interview, he said Northern Ireland politicians are out of touch with voters on social issues.
He said he will intervene to force Stormont to set up abortion services in Northern Ireland and said he wanted to see Irish language rights enacted.
While Ms Long welcomed his comments, she said a newspaper was not the place to make them.
"Timely interventions by the government are always helpful, but I don't think the Sunday Times is the place to make them, perhaps in private with the respective party leaders would be a more appropriate intervention," Ms Long added.
"When we're in delicate times, of course we need to encourage people to move forward.
"The Irish language Act has been sitting waiting to be dealt with now for the last 15 or 16 months. It's time that we got on with it and got it delivered.
"It only gets more difficult for those who have a problem the later in the term it goes.
"I am not sure that broadsides across people's front in the papers is the way to deal with these things, there is a degree of diplomacy required."