The statement gave no indication of when Medvedev might sign.
Earlier in the day, Saakashvili had accused Russia of using cluster bombs and weapons of mass destruction during fighting which broke out last week in the breakaway region of South Ossetia.
He had also criticised the West for not granting Georgia Nato membership earlier this year, saying Russia had stepped up its military presence in the region following the decision.
In his joint news conference with Rice in Tibilisi, the Georgian president said: "We will never, ever surrender, give up our freedom and territory, we will definitely get rid of these invaders for good. I am totally convinced of that."
"Unfortunately today we are looking evil in the eye. It is very strong, very nasty and very dangerous."
Rice said Russian forces should leave Georgian territory immediately and that Russia's president had "not honoured" his promise to halt military operations in Georgia.
|Rice has called on Russia to start withdrawing immediately [Reuters]
"The verbal assurance that President Medvedev gave that Russian military operations had stopped ... clearly was not honoured.
"With the signing of this accord, all Russian troops, and any paramilitary and irregular troops that entered with them must leave immediately," Rice said.
Jonah Hull, Al Jazeera's correspondent in Tbilisi, said: "Saakashvili's public statements are aimed at domestic consumption ... they are for the Georgia public to listen to. And in terms of rhetoric the Russians are doing the same."
On Friday, Russian troops were still said to be stationed in Gori, Georgia's second city, the Black Sea port of Poti, and the western town of Zugdidi, which lies near another breakaway region, Abkhazia.
A Russian convoy was also seen advancing to within 55km of Tbilisi on Friday.
Rice said that international observers needed to be brought into Georgia quickly to stabilise the situation.
Meanwhile, Viktor Yushchenko, Ukraine's president, said on Friday that he had requested urgent talks with Moscow on the Russian navy's use of Sevastopol, a Ukrainian port, as the base for its Black Sea fleet.
On Thursday, Ukraine had said it would make Russia seek official permission for movements of its warships based in the former Soviet state despite Moscow's objections.
Marc Garlasco, from the New York-based Human Rights Watch organisation, told Al Jazeera that both Russia and Georgia were using indiscriminate weapons in the conflict, including cluster bombs.
|Russian soldiers on the road leading to Zugdidi, a major town in western Georgia [Reuters]
Speaking in Tbilisi, Garlasco said: "We've been very concerned that both sides have not been following the Geneva Conventions, and supporting international humanitarian law here.
"It's quite shocking that in the year that 107 countries have agreed to ban cluster bombs, that the Russians are using them in this conflict now.
"Clearly we need to have some international body come here and do some credible investigation.
"Just to look at statements of casualties – the Russians are claiming 2,000 dead in South Ossetia - our investigation has shown 44 at this point. So we really need to have someone discern what the truth is."