The Labour leader is a long-standing supporter of Irish unification and was criticised by many in his own party for his close Republican links during the Troubles.
Mr Corbyn's spokesman said: "It's absurd that we still have this undemocratic anachronism in the 21st century and when Labour is elected we will carry through that pledge".
David Cameron's Conservative government campaigned for Scotland to remain in the United Kingdom ahead of the Scottish independence referendum in 2014, but Mr Corbyn said he would not take that approach.
"We would be ensuring the Good Friday Agreement is carried out to the letter".
Northern Ireland's rudderless public services were thrown into sharp relief recently when a Civil Service decision to approve a major incinerator project in the continued absence of powersharing ministers was overturned by a court.
The Labour leader visited an Irish border bridge on Friday as part of his two-day tour of the country.
So let me be clear, Labour will not support any Brexit deal that includes the return of a hard border to this island.
In addition, he opposed the creation of a customs and regulatory border in the Irish Sea, proposed by the European Union bloc.
Jeremy Corbyn Makes First Official Visit To Northern Ireland
A major sticking point is what arrangement will be put in place if the border can not be solved in an overall deal. We need all sides to come together and make devolution work again.
He argued that the best way to avoid border checks is through a UK-EU customs union - which would offer the UK a say on future trade deals - coupled with a "new and strong relationship" with the EU single market.
The Labour leader added that "maintaining an open border is not just about avoiding paperwork or tariffs, but serves as a symbol of peace". It also has symbolic significance, he said.
The porous 300-mile frontier is one of the most vexed issues facing negotiators in Brussels but Northern Ireland has no ministers to intervene since devolved Government at Stormont collapsed more than a year ago.
The Labour leader wants the British-Irish Intergovernmental Conference to be convened if the stalemate in N Ireland continues.
"The British government is making a mess of these negotiations".
Convening the BIIC is favoured by nationalists, but opposed by the DUP and the Ulster Unionist Party (UUP) who regard it as a "talking shop".
In his first visit to Northern Ireland as Labour leader, Jeremy Corbyn will say Labour will not support a Brexit deal that imposes a hard border between Northern Ireland and the Republic of Ireland.
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