BUDAPEST, April 15, 2018 (Reuters) - Tens of thousands of Hungarians protested in Budapest on Saturday against what organisers said was an unfair election system that gave Prime Minister Viktor Orban a landslide victory at the polls after a "hate campaign" against immigrants. Orban won a third straight term in power in Sunday elections after his anti-immigration campaign message secured a strong majority for his ruling Fidesz party in parliament, giving him two-thirds of seats based on preliminary results. In a Facebook post before the rally, organisers called for a recount of ballots, free media, a new election law, as well as more efficient co-operation among opposition parties instead of the bickering seen in the run-up to the vote. The protest was among the biggest in Hungary in recent years, similar in size to a mass rally prompted by Orban's plan to tax internet use four years ago and a pro-government demonstration called by Orban supporters shortly before the election. Fidesz received 49 per cent of national party list votes and its candidates won 91 of 106 single-member constituencies, most of them in rural areas. Leftist opposition candidates carried two-thirds of the voting districts in Budapest. There was a similar split between ages, with support for Orban's Fidesz at 37 per cent among voters below 30, rising gradually to 46 per cent among those older than 50, according to a survey by think tank Median published earlier this week. The Organisation for Security and Co-operation in Europe has said the election did not offer opposition parties a level playing field amid a host of problems marring a vote that nonetheless generally respected fundamental rights. In their Facebook post, the rally's organisers said: "Fidesz's election system and the government's hate campaign have pushed the majority into a one-third (parliamentary) minority." Protesters marched from the Opera House, a 19th century Neo-Renaissance palace on a majestic downtown avenue, to Parliament by the Danube River, waving Hungary's tricolour flag and the European Union flag, accompanied by whistles and horns blaring.