The Syrian Government must understand that it cannot use assassinations, Foreign Secretary Jack Straw has said.
Mr Straw joined Ms Rice for a tour of Alabama
He and his US counterpart Condoleezza Rice held a joint interview after claims of Syrian links to the murder of Lebanese ex-PM Rafik Hariri.
A UN report into the death will be discussed by the Security Council. Mr Straw said this was a "sharp message" that such behaviour was unacceptable.
Ms Rice said the issue "can't be just left lying on the table".
UN investigators said they had also found evidence of Lebanese collusion in Mr Hariri's death last February.
The Lebanese Government has rejected those claims and Syria says the UN report is "far from the truth".
But Ms Rice told BBC One's Politics Show there was at the least evidence of Syria failing to cooperate, as well as the "very strong implication" it was involved in assassinating Mr Hariri.
Mr Straw said he could not discuss the details of any UN resolution against Syria.
The "mere fact" ministers were holding a meeting at the Security Council about the issue sent a "very sharp message indeed" that such behaviour was unacceptable.
"We know from the history of dealing with Syria... that where the international community is firm and united in the end the Syrian Government gets the message," said Mr Straw.
"And they have to get the message that you cannot have a government, if I may say so, at any level going into assassinations."
He said it was "very serious" that people at a high level in the Syrian regime had been implicated and that there was evidence of false testimony by senior figures.
Record of black leaders
Mr Straw this week joined US Secretary of State Ms Rice in a tour of her home state of Alabama.
In the interview, they both rejected calls for a timetable for withdrawing troops from Iraq but insisted progress was being made in building up Iraqi security forces.
The aftermath of Hurricane Katrina has provoked claims that the US is still a racist society.
Ms Rice accepted there were still poverty problems, some of which were linked to poverty and race.
But she said the US had many company chief executives and political leaders - and its last two secretaries of state had been black.
Mr Straw added: "It's a better record that the UK. We're proud of what we've been able to achieve in the United Kingdom, but we've had fewer black Cabinet members, fewer black leaders."