In her resignation speech, Ms Foster said Northern Ireland will only move forward when the region’s differing “identities” are respected by all.
But a stand-off on the vexed issue of Irish language legislation has the potential to derail power-sharing arrangements unless a resolution is found within the next seven days.
Ms Poots suggested it would be “inappropriate” for Sinn Fein to demand an Irish language act – which would give the Irish language equal status to English – in return for a smooth nomination process.
“We cannot be in a circumstance where we have pre-conditions set for the selection of our first minister,” Mr Poots told BBC Radio Ulster on Monday. “I’m not setting pre-conditions to the selection of Sinn Fein’s deputy first minister.”
Newly-elected DUP chief Mr Poots wants his party’s Paul Givan to become first minister – but Sinn Fein must nominate a deputy first minister for that to happen under power-sharing rules.
The joint nature of the office Mrs Foster has shared with deputy first minister Sinn Fein Michelle O’Neill means Ms O’Neill must also be re-nominated to her role within those seven days.
If one of the parties fails to renominate within the time period, then a functioning executive cannot be formed and the UK government assumes responsibility to call a snap election in Northern Ireland.
“Our community is at a very tense situation at this moment in time,” said Mr Poots. “We saw riots on the streets of Belfast earlier this year. And I have serious concerns about the potential for conflict once again on our streets.
He added: “Not only if Sinn Fein do not nominate the deputy first minister are all of those issues not going to be served well, we are putting our very peace at risk as a consequence of that action.
“If Sinn Fein are going to play fast and loose with the very peace that people enjoy at this moment in time, then that is a very, very serious consideration for them to take. Hopefully they won’t.”
A Sinn Fein source said the party believed Mr Poots was being “disingenuous” in his public comments about an Irish language act – a commitment made as part of the New Decade, New Approach power-sharing agreement of 2020.
The source told the Press Association: “We do not believe they will deliver on the Irish Language Act. Our position is that the nomination for first minister and deputy first minister has to be accompanied by legislation on the Irish language.”
Sinn Fein has demanded immediate action on the Irish language, insisting the legislation must be tabled at Stormont ahead of the summer recess if it is to become law before the end of the current assembly mandate next spring.
Political opponents united briefly at Stormont on Monday to pay tribute to Ms Foster upon her resignation as first minister.
Making her resignation speech, the ousted DUP leader said: “We can poke each other in the eye and have a competition of ‘my identity is better than yours’. But it is only by respecting each other’s identity that we will move forward.”
Ulster Unionist leader Doug Beattie said Ms Foster she had always carried herself with the “utmost dignity,” while SDLP minister Nichola Mallon said she will have inspired young girls to realise there should be “no limit on their ambitions”.