The Foreign Secretary warned that sanctions were still an option unless there was evidence of Russian efforts to de-escalate the crisis within the next few days.
Hopes of progress following the diplomatic deal suffered a setback as pro-Russian insurgents in Ukraine's east said they will leave occupied government buildings only if the interim administration in Kiev resigns.
Denis Pushilin, a spokesman of the self-appointed Donetsk People's Republic, told reporters that the insurgents do not recognise the Ukrainian government as legitimate.
Mr Hague said the government in Kiev had begun work on meeting the conditions of the agreement reached between Ukraine, Russia, the EU and US in Geneva and called on Vladimir Putin's administration in Moscow to do the same.
"We do want to see, over this weekend, Russia take the necessary actions to reduce tensions, to make sure the agreement at Geneva yesterday is upheld," he said.
"We believe that Russia contributed to destabilising the eastern Ukraine over the last week; now it is an important obligation on them to contribute to stabilising it.
"We will all want to see evidence of that, otherwise we will return to imposing more sanctions on Russia, as we agreed at the beginning of the week."
He said the Geneva deal was an opportunity for all involved to "step back from the brink".
"We should welcome that agreement but stress the need for implementation," he said. "This doesn't mean the Ukraine crisis is over; it does perhaps mean that the crisis is entering a new phase."
Mr Hague told the BBC that Moscow had a "great deal of influence" over the opposition forces in eastern Ukraine and "we are absolutely sure that Russia took part in what happened over the last 10 days - the arms, the equipment, the training, the co-ordination".
He added: "There have been denials, but of course there were Russian denials at the beginning that it was Russian forces involved in the Crimea and now it's openly acknowledged by President Putin.
"So we are convinced of that and since Russia contributed so much to destabilising eastern Ukraine over the last week, they can contribute to stabilising it and so we look to them to do so."
The agreement, reached after seven hours of negotiation in Geneva, requires all sides to refrain from violence, intimidation or provocative actions.
It calls for the disarming of all illegally armed groups and for control of buildings seized by pro-Russian separatists to be turned back over to authorities.
It also gives amnesty to protesters who comply with the demands, except those found guilty of committing capital crimes.
Monitors from the Organisation of Security and Co-operation in Europe (OSCE) will be tasked with helping Ukraine authorities and local communities comply with the requirements in the agreement.
David Cameron spoke to US president Barack Obama by telephone to discuss the situation.
Number 10 said: "They agreed that the outcome of the Geneva meeting represented a positive step forward, but that it was essential that the agreements reached were rapidly implemented."
Meanwhile, Russia's envoy to the European Union said the authorities in Kiev had incorrectly interpreted an international deal to resolve the crisis in Ukraine.
"If we are speaking about how the Geneva document is being interpreted in Kiev by the current authorities, then unfortunately they understood this incorrectly," Vladimir Chizhov said.
"In particular, that it only applies to the eastern and southern provinces and those who are demanding federalism, but not to Kiev, where (it thinks) everything is legal including the ongoing occupation of Maidan (Independence Square)."