* Milan stocks rise on hopes of Draghi becoming next PM * Daimler jumps on plan to spin-off truck business * GSK slides; warns of bigger than expected fall in 2021 earnings (Updates to close) Feb 3 (Reuters) - Italian shares posted their best session in four weeks on Wednesday after former European Central Bank chief Mario Draghi accepted the task of forming a new government, while a surge in German carmaker Daimler lifted an index of broader European shares. Milan’s FTSE MIB index closed up 2.1%, while Italy’s 10-year bond yield tumbled. Draghi said he was confident of securing sufficient backing in parliament after President Sergio Mattarella sought his help after hearing that efforts to salvage the collapsed coalition of Prime Minister Giuseppe Conte had failed. ADVERTISEMENT “It may not all be plain sailing and some uncertainties and negotiations remain. But... markets like the news of well-known central bankers at the helm of government,” said Maria Paola Toschi, global market strategist at J.P. Morgan Asset Management. “For the economy, avoiding lengthy further attempts to form a government should mean that critical near-term issues can be addressed.” Italy has been hit by the COVID-19 pandemic and economic crises against the backdrop of political uncertainty battering the country. On the pan-European STOXX 600 index Daimler was the top boost after unveiling plans to spin-off its trucks business. It rose 8.9% while the broader index gained 0.3%. Germany’s DAX rose 0.7% to hit its highest in two weeks. London’s blue-chip index slipped 0.1% as GlaxoSmithKline slid 6.3% after it warned of a bigger than expected fall in 2021 earnings as the COVID-19 pandemic continues to disrupt other healthcare treatments. But upbeat earnings from other companies helped push gains on the pan-region index to a third straight day, with Novo Nordisk, Siemens AG, Publicis Groupe SA all rising after reporting results. Drugmaker Argenx was the top gainer after it raised $1 billion in capital increase. Also keeping sentiment buoyed was hopes of U.S. stimulus after the Senate took steps to allow Democrats to pass President Joe Biden’s proposed $1.9 trillion COVID-19 aid bill without Republican support. European stocks have been steadily rising along with other major markets after losing more than 3% last week on concerns around the slow roll-out of COVID-19 vaccines in the euro zone. A pause in a social media driven rally that drove up prices of silver as well as certain stocks including GameStop Corp has helped calm worries about potential losses incurred by certain hedge funds causing disruption to markets as a whole. (Reporting by Shreyashi Sanyal in Bengaluru; Editing by Shounak Dasgupta, Kirsten Donovan)