Theresa May is under increasing pressure from all sides to break the impasse in the Brexit talks.
The DUP says there is "work to be done" if it is to agree to plans for the future of the border with Ireland.
Irish PM Leo Varadkar said he was willing to consider new proposals and suggested the UK might put something forward later.
Ambassadors of the 27 EU member states are understood to be "waiting for something from London".
On Monday, Northern Ireland's Democratic Unionist Party - whose support the PM needs to win key votes at Westminster - objected to draft plans drawn up by the UK and the EU.
The DUP said the proposals, which aimed to avoid a "hard border" by aligning regulations on both sides of the border between Northern Ireland and the Republic of Ireland, were not acceptable.
The party has said it will not accept any agreement in which Northern Ireland is treated differently from the rest of the UK.
At a summit next week, European leaders will decide whether enough progress has been made in the negotiations on Ireland, the UK's "divorce bill" and citizens' rights so far to open trade talks.
In their letter, the 19 MPs - who largely backed Remain in the 2016 referendum - say they support the PM's handling of the negotiations, in particular the "political and practical difficulties" relating to the Irish border.
The MPs included former cabinet ministers Stephen Crabb, Dominic Grieve, Anna Soubry and Nicky Morgan, reports BBC.