Business Secretary Greg Clark has had talks in France on the possible deal between General Motors and Peugeot owners PSA.
Mr Clark said he had had “constructive meetings” with the PSA board and French industry minister Christophe Sirugue.
Earlier on Thursday, Mr Clark met executives at General Motors in London.
PSA is in talks to acquire GM’s Europe arm Opel, including Vauxhall, a deal which Germany’s economy minister said on Thursday was likely to go ahead.
Vauxhall employs 4,500 workers at plants at Luton and Ellesmere Port, with thousands more involved in its retail and components chain.
The business secretary met with GM’s president, Dan Ammann, Vauxhall managing director, Rory Harvey, and officials from the Unite union.
After the meeting, Mr Clark said he had been reassured about Vauxhall’s UK operations.
“There is some way to go in discussions between GM and PSA, but I was reassured by GM’s intention, communicated to me, to build on the success of these operations rather than rationalise them,” Mr Clark said.
In a statement, GM said it was in talks with PSA “to build on the success” of Opel Vauxhall and to put it in “the strongest possible position”.
‘Jewel in the crown’
However, Unite union leader Len McCluskey, who joined them for a separate meeting, said afterwards that he had received “no assurances”.
“This is a story that is unfolding – we’ll wait to see what the next instalment is,” Mr McCluskey said.
The Unite leader called Vauxhall “a jewel within the crown” of GM’s European business – which also makes Opel cars – and said the government should make clear it would not “accept a single job loss in Britain”.
He also called on Mr Clark to secure meetings with French and German government officials, or risk being “left on the sidelines”.
“The French government own a considerable stake in Peugeot, and one thing’s clear, they will be arguing and fighting for French jobs,” Mr McCluskey said.
Vauxhall estimates that a further 23,000 people work in its UK showrooms and 7,000 in its UK supply chain.
The possible takeover of GM’s European arm Opel by PSA, which is 14% owned by the French government, has sparked concerns in the UK, Germany and France.
Mr Ammann and GM chief executive Mary Barra visited the Opel headquarters in Germany on Wednesday to answer questions about the deal talks.
On Thursday, Germany’s economy minister Brigitte Zypries told reporters after talks with senior executives from GM and PSA that “I expect it [the deal] to take place”.
The German government is “doing everything we can” to preserve Opel’s domestic plants, she said.
The government of Germany’s Rhineland-Palatinate region, home to Opel’s Kaiserslautern plant, also welcomed the potential creation of a “European champion” on Thursday and indicated it had received assurances from GM.
“There are signals that… no plants in Germany will be closed,” regional Minister-President Malu Dreyer said in a statement.
GM last week reported a loss of $257m (£206m) last year from its European operations.
It was the 16th consecutive loss-making year for GM in Europe, bringing its cumulated losses on the continent since 2000 to more than $15bn.
On Tuesday, PSA, which already works with GM in Europe on several projects, announced a takeover was among “numerous strategic initiatives” being considered.