* Von der Leyen seeks to be first female head of EU executive
* Ambitious social, climate and migrant plans aim to win votes
* EU lawmakers' rejection of von der Leyen would be major setback (Adds socialists)
STRASBOURG, July 16 (Reuters) - Germany's Ursula von der Leyen is poised to become the first female European Commission president after winning over sceptical liberal and socialist lawmakers on Tuesday with her vision of a greener, fairer and rule-based Europe.
Securing liberal and socialist votes on top of endorsement by her fellow conservatives would give her legitimacy, allowing her to tackle controversial issues such as climate change, trade and maintaining democracy in the bloc.
Rejection by the European Parliament would have been a serious blow for the bloc, beset by challenges ranging from trade to Brexit and erosion of democratic norms, and a headache for EU leaders who would have to come up with another candidate in a month.
"My group will support Ms von der Leyen today. We are looking forward to work intensively with her to move Europe forward. There is a lot of work ahead of us. Let's renew Europe together!" said Dacian Ciolos, head of liberal group Renew Europe.
Socialists also gave the thumbs up to the 60-year-old German conservative and mother of seven.
"Following a decision in our Group meeting, we will support @vonderleyen. However, we will be vigilant to ensure that she delivers on the progressive commitments she has made as a result of our pressure," the Socialists and Democrats Group (S&D) said in a tweet.
Von der Leyen, who this week resigned as German defence minister, regardless of the EU lawmakers' decision, needs 374 votes for an absolute majority.
With 182 votes from the conservative European People's Party, two-thirds of the 153 members of the Progressive Alliance of Socialists and Democrats, about 103 of the 108 from the Renew Europe liberals and 14 from Italy's 5-Star Movement, von der Leyen would get about 399 votes, above the 374 needed.
Lawmakers started voting in a secret ballot at 1600 GMT with results due around 1730 GMT.
Her nomination as a compromise candidate as part of horse-trading between EU leaders has angered some lawmakers who had put forward their own candidates.
Von der Leyen set out her climate goals, going further than current targets, in a bid to convince both socialists and liberals. She had already pledged the ambitious targets in letters to the two groups the previous day.
"Our most pressing challenge is keeping our planet healthy. This is the greatest responsibility and opportunity of our times. I want Europe to become the first climate-neutral continent in the world by 2050," she said.
She added she would propose a Green Deal for Europe in her first 100 days in office, turn parts of the European Investment Bank into a Climate Bank and introduce a Carbon Border Tax.
She pledged to complete the bloc's capital market union to provide funding to small- and medium-sized enterprises, embrace a more growth-friendly fiscal policy and guarantee a minimum wage to European workers.
Von der Leyen promised to defend the rule of law, took aim at U.S. tech giants' low tax bill in Europe and said she would update EU-wide norms for tackling the migrant issue.
"We need to address the legitimate concerns of many and look at how we can overcome our differences," she said.
In her biggest cross-party promise, von der Leyen offered to help allow the chamber the right to propose new legislation - currently the Commission's prerogative.
She called for unity, trying to win over the fragmented assembly, where eurosceptics made big gains in May elections and Britain's Brexit party became the biggest in the legislature.
"Whoever wants to see Europe strengthen, grow and flourish will have me as a passionate fighter on their side. But whoever wants Europe to weaken, divide and abandon its values will have me as a bitter opponent," von der Leyen said.
"If we are united on the inside, nobody will divide us on the outside," added von der Leyen, who switched fluently between German, French and English in her speech.
Europe's liberal Competition Commissioner Margrethe Vestager described von der Leyen's speech as "strong, warm and balanced", suggesting that the liberals may be leaning towards a yes vote.
The kind of support von der Leyen gets could complicate her job as head of the EU executive in charge of trade negotiations, economic and climate policy for 500 million Europeans and antitrust rulings involving powerful tech giants.