The Labour leader has said the UK nations and regions must come together to deal with the Covid-19 pandemic.
His comments come after the Welsh government said it would close its border to people travelling from Covid hotspots, including Northern Ireland.
The UK government said the decision was "disappointing".
Sir Keir Starmer told BBC News NI: "I don't want us to go down this route of the four nations enjoying different things and setting up different rules.
"I actually think it's incumbent on the prime minister to bring the four nations together and say how can we solve this as a team of four nations".
On Wednesday, the Stormont Executive announced new measures to fight Covid-19.
Schools are to close for two weeks and pubs and restaurants can only operate a takeaway or delivery service for four weeks.
The Labour leader said government support for the devolved nations is "not enough".
He said the short-term support "will cost far less than the long-term damage if we just let this roll on for weeks and months without it".
In a wide-ranging interview for BBC NI, Sir Keir discussed Covid 19, Brexit and a potential border poll.
On Brexit and the ongoing trade talks, he said: "My message to the prime minister is: 'You said you have an oven-ready deal. Get on and negotiate it and deliver that deal in the national interest'."
Asked if his approach to Northern Ireland would be different from his predecessor, Jeremy Corbyn, who was criticised by unionists for being politically supportive of republicans, Sir Keir said: "I've had the privilege of working in Northern Ireland for five years, working with both communities.
"I know very well, you know, how important this is. And I will always work with both communities.
"I've got a fundamental belief in the Good Friday Agreement, that progress has been achieved under that and I would continue in that spirit."
However, the Labour leader would not be drawn on his party's position, should a border poll take place in Northern Ireland.
'I believe in the UK'
"I am not going to get into a hypothetical discussion like that," he said.
He later added: "I believe in the United Kingdom. I want the union to hold together.
"But I think that it's very important that we don't get into hypotheticals years down the line and we understand communities as they are at the moment."
On the issue of the delayed Troubles pension scheme, he said payments should be made soon.
He said his party would put pressure on the government so that victims and their families would receive monies.
The MP for Holborn and St Pancras became Labour leader in April of this year when he succeeded Jeremy Corbyn.
A lawyer who specialised in human rights cases, Sir Keir was previously Shadow Brexit Secretary under Jeremy Corbyn's leadership.
He was made a QC in 2002 and was the Director of Public Prosecutions before entering politics in 2015.