After talks with South African President Jacob Zuma, Mr Brown said Zimbabwe must show progress in key areas including democratic reforms.
President Zuma, on a state visit to the UK, has suggested sanctions should be eased to help Zimbabwe “move forward”.
Mr Zuma later addressed a special meeting of MPs and peers in Parliament.
After their meeting in Downing Street, President Zuma and Gordon Brown sought to present a united front on Zimbabwe, with the prime minister praising South Africa’s role in helping bring “stability and change” to its neighbour.
But the BBC’s Worlds Affairs Correspondent Mike Wooldridge said the two effectively disagreed over the issue of international sanctions and that Mr Zuma had made it clear that if lasting change did not happen in Zimbabwe, some people could use them as an excuse.
President Robert Mugabe and Prime Minister Morgan Tsvangirai formed a unity government last year but remain deadlocked over key appointments.
The ongoing trial of a political ally of Mr Tsvangirai’s for terrorism and treason has also raised tensions.
The EU says sanctions are still needed to keep pressure on Mr Mugabe to live up to his commitments on political and economic reform.
But Mr Zuma has said easing the measured could help the country resolve outstanding political differences.
Mr Brown said some sanctions had been lifted and those remaining in place targeted individuals with a history of supporting violence not ordinary Zimbabweans.
It was “vital” that commissions set up by the government to increase protection for human rights and freedom of speech and to support democratic institutions concluded their work quickly, he said.
“The UK has always said we are ready to support progress on the ground,” he said.
“But we must be absolutely sure that progress is being made. We must be moving from what is a unity, transitional government to free and fair elections.”
Mr Zuma said he was “very positive” that progress was being made in Zimbabwe.
He added that the international community now had a “better understanding” of what was happening in the country.
This week, the US announced it would extend sanctions on Zimbabwe for another year, saying its protracted political crisis remained unresolved despite the power-sharing agreement.
Both the EU and the US maintain a travel ban and asset freeze on President Mugabe, his wife and inner circle in protest at disputed elections and alleged human rights abuses by his government.
Other issues discussed by Mr Brown and Mr Zuma included the global economy, trade links, climate change, nuclear non-proliferation and the upcoming football World Cup in South Africa.
The British prime minister praised preparations for the event and urged South Africa to use the “impetus and momentum” of the tournament to ensure that every child in the country could have access to primary education.
On day two of his three-day state visit to the UK, President Zuma later visited the main site of the 2012 Olympics in east London as well as anti-racism and crime reduction projects in the capital. BBC