People could be allowed to hold hands with their relatives in a care home before they've received their second vaccine dose.
Care Minister Helen Whately suggested that some restrictions on visits could be lifted soon.
With a 12-week delay between the first and second doses, Ms Whately said "I want us to open up sooner than that", suggesting that some of the restrictions could be eased in the coming months.
She said "even if it's to be able to hold hands again ... I really want to make that happen".
All care home residents and staff in England have been offered vaccines, according to the Government, but there is a 12-week gap between doses.
During the lockdown, visits are restricted to taking place outdoors or through substantial screens.
Ms Whately told Sky News: "I really, really want to open up visiting in care homes more.
"To be clear, we have made sure that visiting can continue even during this national lockdown but I recognise it's not the normal kind of visiting - it's having to use screens, or visiting pods, or through windows of care homes that don't have those facilities.
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"Also, we have put funding into social care to help care homes have these facilities, and have extra staff if they need to supervise.
"What I want to do as we come out of the national lockdown is also increase the amount of visiting.
"I don't see that we have to wait for the second vaccination dose, I want us to open up sooner than that."
She indicated that the approach would be "cautious" as most residents will only have had their first dose of vaccine "so it will be step by step".
She said: "I'm determined, so that we can see people go back to - even if it's to be able to hold hands again and see somebody who you haven't been able to see very much in the last few months and over the last year - I really want to make that happen again."
She told LBC she expects the rules on care home visits to be covered as part of the "road map" out of lockdown which Prime Minister Boris Johnson will set out on Monday.
Ms Whately told the BBC that visitors to care homes will still be expected to wear personal protective equipment (PPE) even if visiting rules are relaxed.
She said: "There is still a way to go to see, for instance, whether the vaccine stops people from being infectious and how it plays through.
"Visiting will be taken step by step and we will, for instance, when people come back to more normal visiting, still be asking people to use PPE and follow those kinds of procedures.
"I don't want to have to wait for the second vaccination dose. Clearly, that's really important to give care home residents maximum protection, but I really want us to be able to open up cautiously and carefully.
"To enable residents some contact with family members, because I know it's just so, so important."
