In a 6.19am tweet, the president said: “Mexico should move the flag waving Migrants, many of whom are stone cold criminals, back to their countries.
“Do it by plane, do it by bus, do it anyway you want, but they are NOT coming into the U.S.A. We will close the Border permanently if need be. Congress, fund the WALL!”
It comes after US troops fired tear gas at migrants and suspended all crossings at the San Diego-Tijuana entry point.
Mexico has pledged to ramp up security near the border, where 39 migrants were arrested after a peaceful march descended into chaos on Sunday.
Mexico’s Interior Ministry vowed to immediately deport those it claimed had “violently and illegally” tried to enter the US from Tijuana. It detained three-dozen migrants for alleged breach of peace.
Other migrants returned to the sports complex in Tijuana where more than 5,000 Central Americans have been camped in makeshift shelters since travelling to the border in a caravan.
Activists and Democrat politicians condemned “shameful” scenes after families with young toddlers were pictured fleeing from fumes near frontier fences.
Lurbin Sarmiento, 26, of Copan, Honduras, said her four-year-old daughter was left “choking” by tear gas fired by US border forces.
Agents reportedly fired tear gas as some migrants tried to break through a small hole in wire fences on the Mexican site of the frontier. Fumes were carried by the wind towards people hundreds of feet away.
“We ran, but the smoke always reached us and my daughter was choking,” said Ms Sarmiento.
The chaotic scenes unfolded after a large group of migrants began a peaceful march to appeal for the US government to speed up processing of asylum claims for Central Americans in Tijuana.
Mexican police kept them from walking over a bridge leading to a port of entry into the US, but migrants pushed past officers to walk across the Tijuana river below the bridge. They walked along the river to an area where only a bank of earth and concertina wire separated the migrants from US Border Patrol agents.
Some saw an opportunity to breach the border crossing, prompting US troops to fire several rounds of tear gas.
“We ran, but when you run the gas asphyxiates you more,” said Honduran Ana Zuniga, cradling her three-year-old daughter Valery in her arms.
Footage of the scenes provoked anger in the US.
“This is so incredibly shameful. Seeking asylum is not a crime,” said Black Lives Matter co-founder Alicia Garza. ”Shooting tear gas at asylum seekers lacks a basic level of humanity. This is your government. This is our government. Do not look away.”
Brian Schatz, a Democrat senator for Hawaii, said: “Anyone uncomfortable with spraying tear gas on children is welcome to join the coalition of the moral and the sane. We can argue about other stuff when we’ve got our country back.”
In a separate incident, a 26-year-old Guatemalan woman was injured after falling onto sharp fencing as she tried to enter the US with her two young children east of the San Ysidro port of entry on Friday.
The mother was taken to hospital and her children, aged three and five, were taken into custody by US Border Patrol.
The US said it would maintain a “robust” presence along the southwest border.
Homeland security secretary Kirstjen Nielsen vowed authorities “will not tolerate this type of lawlessness and will not hesitate to shut down ports of entry for security and public safety reasons”.
Mr Trump has repeatedly suggested without evidence that the migrant caravan was full of hardened criminals. In fact, most are poor people with few belongings fleeing gang violence or poverty.
Tijuana mayor Juan Manuel Gastelum on Friday declared a humanitarian crisis in his border city of 1.6 million, which he says is struggling to accommodate the crush of migrants.