It comes two days after Mugabe sacked his deputy, Emmerson Mnangagwa.
Zimbabwe President Robert Mugabe, centre, smiles as he arrives for a a solidarity rally in Harare, Wednesday, Nov. 8, 2017.
Ruling ZANU PF secretary for administration and Finance Minister Ignatius Chombo also told a hastily organised rally in Harare on Wednesday to "show solidarity" with Mugabe for firing Mnangagwa that the ex-vice president "is understood he skipped the border to the neighbouring Mozambique".
The war veterans' leader said this from South Africa at a press conference with global media on Wednesday.
The association of former fighters for independence is loyal to Mr Mnangagwa.
Zimbabwe's fired vice president says he has left the country after receiving threats but he vows to return to lead the nation.
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The war veterans' statement uses language similar to that used by Mugabe's guerrillas during their fight against white minority-ruled Rhodesia in the 1970s.
The apparent hounding of the influential politician into exile by President Mugabe has brought anxiety in a country already buffeted by years of economic, social and political instability. Now Mugabe's wife appears poised for the role.
Mnangagwa's removal on Monday was a boost for Mugabe's wife, Grace, who has been a vocal critic of the former vice president and is seen as a potential successor to her husband.
"We have kicked him out for the same reasons", the president said.
Mugabe is due to address the crowd of supporters who've held up banners announcing their support for First Lady Grace Mugabe to become the new vice president.