Talks are under way with South Korea and Australia to establish "green lanes" for travel in the Covid-19 environment, said Trade and Industry Minister Chan Chun Sing.
Singapore is also having such discussions with New Zealand and Malaysia, while China on Friday became the first country to establish a green lane with the Republic.
Mr Chan said Singapore is in simultaneous discussions with "as many countries as possible" on forming green lanes, and that such discussions are taking place on a bilateral level, not a multilateral one.
"We are happy that we have been able to swiftly work on arrangements with China, and we hope to make progress with the rest of the countries," he said.
Such arrangements allow for the restoration of connectivity and facilitation of short-term essential business and official travel between countries, subject to safeguards against the coronavirus.
Mr Chan said there were several considerations that go into deciding which countries to enter into such agreements with.
"Reciprocal green lane agreements mean there must be mutual assurance of each other's test protocol and standards," he said.
He explained that a situation where there is no such trust and "everybody does their own thing", with each country insisting on testing travellers for the virus as well as giving them a 14-day quarantine, would be essentially unworkable.
This is because aside from having to undergo two tests, travellers would have to be quarantined for almost an entire month in order to travel from one place to another.
So for a green lane arrangement to work, both countries would have to first have confidence in each other's safeguards and be able to coordinate their quarantine orders, so that travellers might need to be tested or quarantined only once.
Aside from discussing necessary protocols, there is also a need to look at the health situation in each country to see when these protocols can be safely deployed, he added.
Mr Chan was also asked how the United States' decision to end its preferential treatment of Hong Kong - often pitted as a rival financial hub to Singapore - would affect the Republic.
He said: "We don't yet have all the details about what the US intends to do, so I won't be able to comment on that. We're closely monitoring the situation and when we have more details from the US side, then we'll be able to make an assessment.
"We wish Hong Kong well and we hope that they can continue to do well as one of the business hubs in East Asia."