Lib Dem, SNP, Plaid Cymru and Green Party leaders are tabling the amendment.
He told ITV's Peston on Sunday: "The single market is dependent on membership of the European Union".
If the Labour party announced tomorrow that we would keep Britain in the single market and customs union, it would be a game-changing moment in British politics.
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The United States also joined the non-binding agreement under President Barack Obama, but Trump said past year he was withdrawing. Trump's meeting with Solberg was the first foreign leader visit with the president in 2018.
Streeting is one of a well-coordinated group of vocal backbench rebels campaigning for leader Jeremy Corbyn to harden Labour policy by saying he would back continued membership of the single market and the customs union.
Other Labour have figures - including the party's Deputy Tom Watson - have repeatedly refused to rule out another vote.
Emily Thornberry, the shadow foreign secretary, suggested on BBC's Andrew Marr Show that Labour could end up supporting a second vote if it became clear a substantial proportion of the public backed remaining in the EU.
The Labour leader said his party were not in favour of another vote at the moment - but wouldn't be drawn on whether he would stick to it in future.
"It's heartening to see parties working together to halt the calamitous Tory Brexit plans", Green Party joint-leader Caroline Lucas added. "What we've called for is a meaningful vote in Parliament and that is the one area that I think Parliament has asserted itself in the vote before Christmas". "We urge the leadership of a fifth opposition party, Labour, to join us so we can change course from the unsafe Brexit being pursued by the Conservatives".
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The tentative deal also addresses border security, including a border wall , the diversity visa lottery and chain migration. Most Democrats and nearly all Republicans say that they favor better enforcement of laws against illegal immigration.
Mr Corbyn expressed concern about some parts of the single market set-up.
MPs such as Chuka Umunna, Stephen Kinnock and Heidi Alexander have all urged the party leadership to embrace a softer form of Brexit.
"If you were to ask the vast majority of Labour Party people what do you actually want to achieve, rather than the label, we'd all be in huge agreement", he said.
The Labour leader said: "The single market is dependent on membership of the European Union".
"Do we have a trading relationship with Europe which is tariff-free, which is based on access to that market, and access of Europe to our market? Yes".
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The White House's announcement coincided with a series of new sanctions by the Treasury Department targeting Iranian officials. Iran said on Saturday it would retaliate against the new sanctions, although it did not specify how.
"This amendment would not keep the United Kingdom in the single market and customs union, nor does it intend to deal with the serious flaws in this Bill", they said.
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IN outscored Cleveland 32-16 in the third quarter to erase a 14-point halftime deficit and take a 76-74 lead after three quarters. The Pacers overcame a 22-point deficit in their 97-95 victory over Cleveland, handing the Cavaliers their third straight loss.
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Following the transaction, the executive vice president now directly owns 187,025 shares in the company, valued at $46,892,778.25. Moreover, First Pacific Limited Liability Corporation has 0.26% invested in SM Energy Company (NYSE:SM) for 1.88 million shares.
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Trump gave Congress six months to find a way to allow immigrant approved for the DACA program to remain in the USA permanently. But some of those issues will likely have to wait due to the sense of urgency running through these discussions.
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It is aimed at ensuring Iran uses its nuclear capabilities for peaceful purposes while preventing it from gaining nuclear weapons. Iran has said that if the United States walks away from the agreement, it is ready to give an "appropriate and heavy response".
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United Nations official Rupert Colville added "These are shocking and shameful comments from the President of the United States". On Friday morning, Trump tweeted that he used " tough " language at the meeting, but not the reported vulgarity.