Fiona Byrne's support for a boycott of Israeli goods did not weaken her tenure as Marrickville mayor, a Greens MP says.

The controversial mayor did not contest her position last night, telling councillors she could not afford to feed her family on a mayoral salary of $47,000 plus a car.

Fiona Byrne ... elected not to continue as the mayor of Marrickville. Credit:James Brickwood

She ran as a Greens candidate for the state seat of Marrickville, in Sydney's inner west, but was defeated by the Labor incumbent Carmel Tebbutt by a margin of less than 1 per cent.

Ms Byrne is believed to have lost voter support in the March 26 election, in a seat the Greens were hopeful of winning, because of her support for a state-wide boycott of Israel.