A Reuters correspondent on the scene said three police officers blocked Movement for Democratic Change lawyers Alec Muchadehama and Andrew Makoni from entering the High Court building.
The MDC wants the High Court to order the electoral commission to release results from last Saturday's vote. A long delay in releasing results has roused opposition suspicions that President Robert Mugabe is buying time to organise a fight-back.
There are strong signs that Mugabe's government is preparing for a strong counter-offensive after it lost control of parliament for the first time in his 28-year rule.
"We can't go in. They are threatening to shoot. They are saying no-one enters the court," lawyer Alec Muchadehama told reporters outside the building.
The case had been due to be heard at noon (11:00 a.m. Birtish time). A Reuters journalist said the police appeared to have come from the president's offices opposite the High Court where they were on guard duty.
More police then arrived.
The MDC says its leader Morgan Tsvangirai defeated Mugabe and should be declared president of the economically devastated southern African nation.
Projections by the ruling ZANU-PF party and independent monitors suggest Tsvangirai will fall short of the absolute majority needed to avoid a second round.
Mugabe had looked wounded and on the defensive earlier in the week when ZANU-PF suffered its first election defeat. But a meeting of the party's politburo resolved on Friday to fight back.
It said Mugabe would contest and win a rerun. Party officials also alleged widespread MDC bribery of electoral officials and said they would legally challenge the results in 16 constituencies.
If this succeeded they would regain control of parliament.
The government-run Herald newspaper reported on Saturday that a provincial elections officer had been arrested in Zimbabwe's Midlands region over charges that some polling stations under him had inflated vote tallies for the MDC and recorded lower votes for Mugabe and ZANU-PF candidates.
"ZANU-PF in the province say they are checking every ward as they suspect a wider conspiracy," it said.
MDC spokesman Nelson Chamisa said on Friday the MDC was going to court to force release of the presidential results.
"We want an urgent release of the results, within four hours of the court order," he said. "We're fighting the anxiety, disappointment, speculation and rumours as a result of this delay."
