"If Russia does not step back from its aggressive posture and actions in Georgia, the US-Russian relationship could be adversely affected for years to come," he said.
Gates also said that a US-Canadian-Russian military exercise due to take place on August 20 had been cancelled.
The defence secretary's warning came as there were unconfirmed reports that a large Russian convoy was moving towards Georgia's second city of K'utaisi in the west of the country.
Earlier on Thursday, Russia warned Washington against encouraging Georgia's leaders to take steps that might lead to a repeat of the "tragic scenario" of recent days.
"We expect the United States to adopt a responsible approach," Russia's foreign ministry said in a statement.
"It is especially important to refrain from any steps that could directly or indirectly be taken by the Georgian leadership as encouragement of its revanchist ambitions and prompt a repeat of the tragic scenario."
Jonah Hull, Al Jazeera's correspondent in Tbilisi, the Georgian capital, said that the standoff between Georgian and Russian troops around the Georgian city of Gori could be read as a message to Washington over its involvement in the conflict.
"Russia will be annoyed at America sticking its nose in and we may now be seeing signs of it trying to make a point to the United States," he said.
"The Russians are, of course, deeply annoyed that the Americans have got involved on this level. They would have expected American involvement but not necessarily on this blatant level - Condoleezza Rice is not even paying a visit to Moscow."
Although Gates said he did not foresee a need for US military forces in Georgia, he noted there were US humanitarian relief efforts in the country.
"Right now, the only people we will have on the ground are those that are required to deliver the human mission. Our priority is to save lives and alleviate suffering," he said.
A second C-17 US military cargo plane carrying humanitarian assistance for Georgia arrived in the capital, Tbilisi, on Thursday morning.
George Bush, the US president, earlier re-affirmed that the US remained fully committed to "a sovereign, free Georgia and its territorial integrity".
|Ban Ki-Moon said he was concerned about the humanitarian situation [AFP]
Meanwhile, Ban Ki-moon, the UN secretary-general, said on Thursday that he was concerned about the humanitarian situation, lawlessness and lack of access for aid workers in parts of Georgia.
Ban said the conflict had caused a significant displacement of people and he urged "all sides to control forces under their command to ensure that the current state of lawlessness ceases".
In a statement, Farhan Haq, Ban's spokesman, said: "The secretary-general welcomes the ceasefire agreement reached by the governments of Georgia and the Russian Federation, but notes that notwithstanding this agreement, there are reports of some continuing violence, with civilians bearing the brunt.
"He reminds all parties concerned of their obligation to respect and protect civilians in accordance with international humanitarian law and human rights law.
"All fighting should end immediately and the current state of lawlessness should cease. Moreover, as tensions continue to run high, it is essential that measures be taken to ensure the protection of minority groups throughout Georgia."
Bush's comments came as Rice, the US secretary of state, arrived in France for talks with Nicolas Sarkozy, the French president, en route to Georgia.
In Paris, she issued another call for Russia to honour a ceasefire.
Rice is to take the formal ceasefire agreement to Tbilisi on Friday to have it signed by Mikheil Saakashvili, the Georgian president.
Sarkozy said the documents are "intended to consolidate the ceasefire".
Sarkozy, who has been leading Western diplomatic efforts to end the conflict between Russia and Georgia over the breakaway provinces of South Ossetia and Abkhazia, said the situation on the ground was "improving".
"If tomorrow, President Saakashvili signs these documents, then the withdrawal of the Russian troops can start," he said.
Rice said Russian military actions on the ground indicate the country has not respected the truce.
Meanwhile, members of Europe's security and rights organisation, the OSCE, appeared ready to send up to 100 more monitors to Georgia to help supervise the fragile ceasefire.
"We have discussed this proposal in the permanent council and there is no decision yet, but I can say that there is no objection in principle on this... The decision will be taken as soon as possible," Heikki Talvitie, the OSCE's special envoy for the South Caucasus, said.
Russia, Georgia and the US are all OSCE members.
The OSCE currently has a mission of about 200 people in Georgia, of whom eight are military monitoring officers looking at security, military and humanitarian issues in and around the conflict zone.
Turkey also increased humanitarian assistance for Georgia on Thursday, sending 10 trucks carrying relief supplies to its northeastern neighbour.
The shipments contained food, kitchen kits and clothes, a Red Crescent official said in the northern city of Trabzon, from where the aid was sent.
Recep Tayyip Erdogan, the Turkish prime minister, met Saakashvili in Tbilisi early on Thursday, and promised that Turkish assistance for Georgia would continue.
Turkey has developed close ties with Georgia since its neighbour gained independence following the collapse of the Soviet Union, and supports its bid to join Nato.