Frenchwoman Christine Lagarde was proposed as president of the European Central Bank, while Spanish Foreign Minister Josep Borrell was nominated to become EU foreign policy chief, meaning he would be charged with supervising the Iran nuclear deal, among other duties.
Referring to Von der Leyen, who was Germany's defence minister for six years, Baba said: "She is a very experienced politician".
German Chancellor Angela Merkel said she was entering Tuesday's talks with "new creativity" and urged other leaders to be more open to compromise.
Mr Tusk wants nominations to be wrapped up soon, seeking to prevent further erosion of public confidence in the European Union amid uncertainty over Brexit on October 31, ironically the same day Mr Juncker steps down.
An EU diplomat said the Timmermans proposal had foundered Monday in the face of opposition from the Visegrad 4 plus Italy, where the populist government shares some of the Eastern Europeans' anger at Brussels over migration.
A plan hatched during the G20 summit in Osaka, Japan, by the EU's big guns to install socialist Frans Timmermans as president of the European Commission, while giving conservative rival Manfred Weber the post of European Parliament president has failed to convince.
Mr Weber has the backing of the German Chancellor Angela Merkel.
Already beset by crises over Brexit and damaging infighting over how best to manage migrant arrivals, the EU's 28 leaders had been keen to show there is still life in the European project with quick decisions on a series of top-notch nominations for what are key portfolios.
Czech Prime Minister, Andrej Babis told reporters in Brussels: "We want somebody on the presidency of the commission which doesn't have a negative view on our region, Mr Timmermans is not acceptable for us, that's it". "I hope so", said Tusk, a former Polish prime minister.
The move prompted an angry response from Emmanuel Macron, the French President, who came back to Paris just shortly after the meetings were abruptly called off, terming the impasse as a "failure, until Tuesday's morning".
In a sign that the 28 national leaders were trying to build a compromise to bring to the table, the start of their talks was delayed by four hours until 1300 GMT to allow more time for separate consultations.
Commenting on the announcement of two women as nominees for the top European Union positions, Tusk told reporters at a press conference following the talks: "I am really happy about it".
The discord echoed a wider fracturing of the EU's political center that was evident in May's European Parliament elections that delivered a more fragmented assembly in which no bloc won a majority and far-right and far-left groups performed strongly. "If elected, she will be the first woman to lead the European Commission".
The summit is the third attempt to fill the top post at the EU.
Others mentioned include Brexit negotiator Michel Barnier of France, Greens leader Ska Keller of Germany, Lithuanian President Dalia Grybauskaite and Margrethe Vestager, the EU's competition chief since 2014.