Kit Malthouse, the policing minister and MP for North West Hampshire, said he wanted to see international travel return "as soon as possible".
On Monday the Biden administration announced it will maintain restrictions on a range of countries, including the EU and China, for the foreseeable future.
Both the US and the UK have a high number of Covid-positive cases caused by the Delta variant, although new infections in the UK appear to be decreasing.
“Given where we are today ... with the Delta variant, we will maintain existing travel restrictions at this point,” White House spokesperson Jen Psaki told a press conference.
"Driven by the Delta variant, cases are rising here at home, particularly among those who are unvaccinated and appear likely continue to increase in the weeks ahead.”
Under current rules, British nationals are not allowed to enter the US if they have been in the UK and a number of other countries in the previous 14 days.
The UK has the US on its "amber list" of countries and travel between the two countries has been frozen since March last year.
Responding to the US move to keep restrictions in place, Mr Malthouse said British citizens will have to continue dealing with uncertainty around travel until the pandemic has subsided.
He told Sky News: "Obviously that is for them to assess and we are assessing the likelihood of variants coming in from other countries as well. So, it doesn't surprise me that they are doing similar. It is obviously disappointing."
He added: "We want to get back to international travel as soon as possible. I have got lots of family overseas who I would love to go and visit, particularly in Canada.
"I am afraid that the tail-end of this virus, and let's hope it is the tail-end, we are still coping with some of that uncertainty across the world and people will have to bear that in mind as they decide their travel plans or otherwise."
The US decision came despite intense lobbying efforts from the travel and tourism industries to salvage summer travel for Europeans and others covered by the restrictions.
The extraordinary US travel restrictions were first imposed on China in January 2020 to address the spread of COVID-19 and other countries have been added since then - most recently India in early May.
New Covid cases continue to rise in the US and Dr Anthony Fauci, who has led the country’s response to the virus, said earlier this week that things are “going in the wrong direction”.
Last week, the US Centers for Disease Control and Prevention director Rochelle Walensky said the seven-day average of new cases in the US was up 53 per cent on the previous week.
The more transmissible Delta variant, first detected in India, now comprises more than 80 per cent of new cases nationwide, the CDC said.
Figures show there were 56,635 new cases reported nationwide on 26 July, up from 51,939 in the previous 24 hours.
Positive cases have been steadily rising since the beginning of the month.
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