(Updates with context and detail from marches)
TUNIS, Aug 13 (Reuters) - Around 40,000 secularists rallied in Tunis on Tuesday to call for the departure of the Islamist-led ruling coalition, but there were no reported clashes with another demonstration by thousands of Islamists elsewhere in the Tunisian capital.
Beset by a severe economic downturn, a suspension of parliament and a surge in Muslim militant attacks, Tunisia's government, led by the moderate Islamist Ennahda party, is grappling with secularists' calls for its resignation.
"Go, Go Ennahda ... the people want to bring down the regime," chanted the crowd of mainly female secularist protesters, in one of the largest opposition protests to be held in front of parliament in Bardo Square.
A few kilometres away, thousands of Islamists protested in support of Ennahda in Habib Bourguiba Avenue.
The rival demonstrations had raised fears of violent confrontation in the birthplace of the Arab uprisings.
With polarisation between Islamists and secularists growing, concerns have been growing that Tunisia could drift towards an "Egyptian scenario" in which a disgruntled secular opposition topples an elected Islamist-led government.
The opposition is angry about the assassination of two of its leaders, which officials have blamed on radical Islamists, and has been emboldened by the Egyptian military's removal of Islamist president Mohamed Mursi last month after mass protests against his shambolic rule.
"Tunisian women today are telling the Islamists 'Get out, we want a modern government'," said a protester named Sonia.
For their part, several thousand Islamists marched to put on a show of popular support for Ennahda, chanting "No to a coup, yes to elected leaders".
Tunisia is in the throes of its worst political turmoil since secular autocrat Zine el-Abidine Ben Ali was overthrown in early 2010 in the first of the Arab Spring uprisings.
"We do not see any results after weeks of political crisis, If this political stalemate continues, the result will be clashes on the street," said political analyst Sofian Ben Hmida.
Islamist militants killed eight Tunisian soldiers in an ambush last month and the government, under pressure from secular critics, has responded with raids and air strikes on jihadist mountain redoubts.
Negotiations this week between Tunisia's powerful UGTT union federation, which has good relations with opposition parties, and Ennahda leader Rached Ghannouchi on a way out of the impasse proved inconclusive.
U.S. Ambassador Jacob Walles also met Ghannouchi and Beji Caid Essebsi, a former prime minister and the head of the main opposition Nida Touns party, on Monday to try to narrow the gap between them, but without any concrete result.
Ghannouchi said last week that his party was open to dialogue with secular opponents but that removing Prime Minister Ali Larayedh was out of the question.
The opposition wants to void the transitional parliament that has been drafting a new constitution and electoral law, fearing that it will cement Islamist domination in a country traditionally one of the most secular in the Arab world.
Secularists aim to announce an alternative "salvation government" next week, suggesting little prospect of compromise.
Jilani Hammami, a leader of the opposition Salvation Front leader, said it was close to deciding the line-up of its alternative cabinet and that it would make important announcements during Tuesday's rally.
The head of the transitional parliament, a member of a secular party in the unsteady government coalition, suspended the legislature a week ago in protest at a lack of meaningful talks between Ennahda and the opposition.
Tunisia's army may have played a role in Ben Ali's overthrow by refusing to shoot demonstrators, similar to the role of Egypt's military in helping protesters to oust autocratic president Hosni Mubarak in 2011.
But Tunisia's armed forces do not have the large and lucrative stake in the economy that Egypt's military do and have not traditionally intervened in politics, so are unlikely to loom large in the fate of the Islamist leadership in Tunis. (Reporting by Tarek Amara; Writing by Dominic Evans; Editing by Kevin Liffey)