The European Parliament is expected to issue a full response to Britain's alternative Brexit offer later.
British Prime Minister Boris Johnson wants to get rid of the backstop - which aims to prevent a hard Irish border.
Instead, he proposed Northern Ireland follow European Union regulations for at least four years but leave the customs union - meaning checks would be required on some goods crossing the border.
It would also ask the Northern Ireland institutions at Stormont to vote on whether they wished to remain under the plan every four years.
This is a vote in which the DUP would hold a veto over.
The Taoiseach Leo Varadkar and top officials from the EU's commission and parliament have already rejected the proposals.
In a phone call on Wednesday, Mr Varadkar told his British counterpart the proposals "do not fully meet the agreed objectives of the backstop".
But he said he would study them in further detail, and consult with the EU institutions.
Mr Varadkar expects to speak with European Council President Donald Tusk, European Commission President Jean-Claude Juncker and with other EU heads of government over the coming days.
In Brussels, after a meeting of senior EU officials and MEPs, Guy Verhofstadt, who chairs the European parliament's Brexit steering group, said they were "absolutely not positive" about Mr Johnson's plan.
"It doesn't provide the necessary safeguards for Ireland," he said.
After he also spoke to Mr Johnson by phone, European Commission President Juncker welcomed the proposals for "full regulatory alignment" between Northern Ireland and the EU.
"However, the president also noted that there are still some problematic points that will need further work in the coming days, notably with regards to the governance of the backstop," a statement said.
"The delicate balance struck by the Good Friday Agreement must be preserved."
Earlier, EU chief negotiator Michel Barnier told reporters: "There is progress. But to be frank, a lot of work still needs to be done to reach, to fulfil, the three objectives of the backstop - no border, all-Ireland economy, and protecting the single market.
"That means protecting the consumer, the citizens, and the businesses inside the single market, the 27 member states.
"So now we will continue to work, to work to reach a deal. The no-deal will never be the choice of the EU. Never. So we will continue to reach a deal and to work with the UK team."
Mr Johnson is also facing pressure from opposition parties in London to make a House Commons statement on his proposals.
UK Labour leader Jeremy Corbyn claimed the proposals were worse than those of Theresa May.
"It's worse than Theresa May's deal," he said.
"Everything to do with his behaviour and his language over the past few weeks has been about getting a no-deal Brexit."
"I'm sure he knows full well that what he's put forward is unlikely to be approved," Mr Corbyn said.
Additional reporting: IRN