The resolution submitted by a shareholder would have forced Maersk to publish human rights risk assessments it carried out ahead of the transfers, and a second to halt arms transfers to Israel.
A summary of the annual general meeting of shareholders said the measures, which had the support of over 70 NGOs including Amnesty International, Oxfam Denmark and ActionAid, had failed.
Maersk, which has a contract with the US government, reiterated at the annual general meeting of shareholders that it does not transport weapons or ammunition into conflict zones.
However Maersk said "we recognise the need for enhancing our approach to human rights risk assessments when operating in conflict-affected areas."
The resolution submitted by Zen Donen follows a report produced by investigative media Danwatch which alleged Maersk transported tanks, equipment, and ammunition.
In November, a Maersk container ship was denied entry to the Spanish port of Algeciras on the grounds that it had transported weapons for Israel, which the company denied.
Spain has refused permission for ships carrying weapons destined for Israel to dock in its ports since the spring of 2024.
Activists were expected to demonstrate in front of Maersk's offices on Tuesday evening.
"We're not going to let up pressure until Maersk stops being complicit with what we consider genocide," said Sophia, an organiser of the demonstration.
In February, 20 people were arrested at a protest outside Maersk headquarters in Copenhagen that was attended by Swedish climate activist Greta Thunberg.
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