Fans danced and waved blue and yellow national flags in the rain in Kiev on Monday as Ukraine made amends for a terrible World Cup start by demolishing Saudi Arabia 4-0 in their second Group H match.

Ukrainian fans celebrate as they watch their team defeat Saudi Arabia on giant screen in Kiev.[Reuters]

However, the celebrations were low key and tinged by the realisation that the squad, making their first World Cup appearance, still have to face Tunisia in their final group game with more formidable foes to come if they make the last 16.

Some 10,000 fans, despondent at the 4-0 drubbing by Spain in their team's opener, cheered wildly under umbrellas in front of a giant screen in Independence Square -- focal point of Ukraine's 2004 Orange Revolution -- as Andriy Rusol and Serhiy Rebrov put Ukraine ahead before halftime.

After team mainstay Andriy Shevchenko and midfielder Maksim Kalinichenko scored in the second half to turn the match into a rout, drenched fans formed a vast circle for a victory dance.

Cars raced up and down city centre streets, horns tooting, but supporters quickly made their way out of the square. Smaller crowds gathered in Lviv in western Ukraine and in Donetsk in the industrial east -- Ukraine's second big soccer town.

Riot police were at the ready in Independence Square, steering a group of extreme right-wing protesters into a corner.

Fans whow ere upset after the Spanish debacle praised the players this time.

SAUDI RUINS

"Saudi Arabia lies in ruins. We want to take on the whole world and win!" a fan from eastern Ukraine wrote on a popular sport Web site.

Commentators were relieved at the turnaround but guarded in their optimism.

"Let's not forget that Saudi Arabia is not Tunisia. We still have that ahead of us," Anatoly Popov, executive director of Ukraine's Professional Soccer League, told Fifth Channel television.

"Ukraine played to only 60 percent of its capabilities. We still have problems to contend with on defence. And we are still looking for the optimal lineup. If there is no excessive euphoria we can beat Tunisia," he added.

Oleg Salenko, a former player for Dynamo Kiev and the Soviet national squad, also injected a note of caution.

"It must be said that Saudi Arabia and Tunisia are the sort of teams Ukraine should not lose to under any circumstances," he told Fifth Channel.

Ukraine were the first European team to qualify for the finals in Germany but coach Oleg Blokhin has tempered expectations, saying his immediate aim is to advance from the group stage.

Not all the fans where ecstatic either with many pointing to several missed chances in the final stages of the game.

"What a bunch of clowns. How many chances did they squander?" wrote one fan from western Ukraine. "This is only possible in the Ukraine premier league. If we play like this against Tunisia, there is no chance."