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Travel industry figures have dismissed the latest moves by the US and UK to reopen travel.
A new taskforce will be set up to make recommendations on easing restrictions as part of an "Atlantic Charter", set to be agreed on Thursday.
A Number 10 statement said the prime minister and president would "work to relaunch UK-US travel as soon as possible".
But the boss of Virgin Atlantic said the announcement "falls short".
Chief executive Shai Weiss said: "The creation of the Atlantic Taskforce is positive recognition of the importance of the UK-US travel corridor and a first step towards reopening the skies."
But he said the lack of a specific time frame for reopening travel meant airlines, businesses and passengers faced a lack of certainty.
Ahead of the start of the G7 summit in Cornwall, Mr Weiss urged Mr Biden and Mr Johnson to allow trans-Atlantic travel no later than 4 July.
What are the current rules on US-UK travel?
Nearly all passengers from the UK are currently banned from travelling to the US.
Under a presidential decree introduced last March, non-US citizens who have been in the UK in the last 14 days cannot enter the country unless a specific exemption applies.
Meanwhile, travellers from the US to the UK must self-isolate for 10 days on arrival as the country is on the "amber list".
Read more on restrictions when travelling to Amber list countries here.
Clive Wratten, chief executive of the Business Travel Association, also called for a firm commitment on a date.
"We welcome the formation of the Atlantic Charter 2021 as a step in the right direction for transatlantic travel.
"However, this is the latest in a long line of travel taskforces which so far have only wreaked further devastation on our industry. Jobs won't be saved, nor livelihoods protected, until we are given a certainty on dates for the resumption of international travel."
A spokeswoman for the Association of British Travel Agents said that "steps to get travel restarted are very welcome". But she also pointed out the lack of detail in the announcement.
She added: "Consideration should also be given to capitalising on the success of the UK vaccine rollout by relaxing rules for fully vaccinated individuals when travelling between low-risk areas, as the US, and many other countries, are already doing."
The taskforce will be overseen in the UK by Transport Secretary Grant Shapps and will be chaired by senior officials in the US and UK.
It will "work to explore options for resuming US-UK travel and ensure that the UK and US closely share thinking and expertise on international travel policy going forward", Downing Street said in a statement.
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It added: "Links between the UK and US are not only crucial for our people, they create and sustain jobs across and throughout our two countries."
In a letter calling for trans-Atlantic travel to reopen on Monday, airline bosses and Heathrow Airport estimated that UK businesses are losing £23m each day that the route remains closed.
Boris Johnson and Joe Biden will also agree to work together on issues such as the post-pandemic recovery, climate change and security as part of Atlantic Charter, which is expected to be agreed when they meet on Thursday in Cornwall.
The original Atlantic Charter was a joint statement made by Winston Churchill and Franklin D Roosevelt in 1941, setting out joint goals in the wake of the Second World War.