Donald Trump has said he would lead America back into the controversial Trans Pacific Partnership trade pact – but only if he was offered a better deal than that negotiated by the Obama administration.

After reports that he was reconsidering his decision to pull out of the pact, Trump tweeted on Thursday night that he would only do so if he was offered improved terms from the 11 existing signatories, who include Japan, Australia and Canada.

“Would only join TPP if the deal were substantially better than the deal offered to Pres. Obama,” he said.

“We already have BILATERAL deals with six of the eleven nations in TPP, and are working to make a deal with the biggest of those nations, Japan, who has hit us hard on trade for years!

Although Japan was singled out for criticism, its trade minister said it would welcome a decision by the US to explore rejoining the TPP.

Japan joined Australia, Brunei, Canada, Chile, Japan, Malaysia, Mexico, New Zealand, Peru, Singapore and Vietnam in signing a reconstituted TPP last month after Trump pulled the US out of the “horrible” Obama-era deal.

Asked about a possible US change of heart, Japan’s trade minister, Taro Aso, told reporters on Friday: “If it’s true, I would welcome it.”

Aso said he expected prime minister Shinzo Abe and Trump to discuss the TPP at their summit meeting next week.

But he added that needed to verify facts carefully.

Trump “is a person who could change temperamentally, so he may say something different the next day”, he added.

Trump had asked his trade advisers to look at rejoining TPP, White House spokeswoman Lindsay Walters said earlier on Thursday. The president withdrew the US from the TPP early last year under his “America First” policy, raising fears of trade protectionism.

“After the US withdrawal, Japan, recognising the significance of free trade, has led the initiative in pulling together the TPP 11,” Aso said.

“Our efforts have borne fruit if the United States judged it would be better to rejoin,” he said.

New Zealand trade minister David Parker was wary of Trump’s apparent U-turn, saying it wasn’t clear yet “how real it is”. Parker said New Zealand was open to the idea of the US joining but “it remains theoretical at this point.”

In Singapore, a spokesman for the ministry of trade and industry said: “The TPP was designed to be an inclusive agreement which is open to like-minded countries willing and able to meet its high standards. Singapore welcomes the US’ interest to rejoin the other TPP parties and achieve the original vision of the Agreement.”

Other signatory nations are likely to welcome US involvement. Before the new deal was signed in Chile in March, Australia’s prime minister Malcolm Turnbull said it would be “great” if the US came back did not expect it to happen quickly. “We’re certainly not counting on it.”

Innes Wilcox, head of the lobby group Australia Industry Group, said it was disappointing the US had not been part of the final deal but hoped Washington “sees the benefits” and signed up in future.