Mr Phillips, 57, disappeared along with Brazilian indigenous expert Bruno Araújo Pereira in a remote rainforest area while researching a book.
The BBC has reported that the pair had received threats days before vanishing on Sunday morning, according to indigenous rights groups.
Both men are said to have deep knowledge of the region.
Mr Phillips has been living in Brazil for more than a decade and is a long-time contributor to the Guardian, Financial Times and Washington Post.
He has written extensively about the threats facing the Amazon, including how cattle farming is fuelling an environmental crisis and how illegal gold miners encroach on indigenous territory.
A Portuguese statement said the two men had been travelling by boat in the Javari Valley to interview members of an indigenous guard.
The area is located in the west of Amazonas state, near the border with Peru, and has seen incursions from illegal loggers and miners.
On Sunday, the pair stopped in São Rafael, where Mr Pereira was scheduled to meet a local leader to discuss joint patrols between indigenous people and residents of riverside communities.
According to the rights groups, Mr Phillips and Mr Pereira arrived at 6am local time and set off shortly afterwards towards Atalaia do Norte, a journey which takes around two hours.
When they failed to arrive, a search party was sent out at around 2pm but found no trace of the two men along the stretch of river they had been expected to take.
The last to see them were residents of São Gabriel, a community downriver from São Rafael, who spotted their boat going past, the statement said.
Police say they interviewed two people who are thought to be among the last to have seen the men, but no arrests were made.
The rights groups say Mr Phillips and Mr Pereira were traveling in a new boat and had enough fuel to cover their journey.
They add that in the week leading up to the men's disappearance, the team had received threats.
The area is home to more than 20 indigenous groups, who have denounced activities by illegal miners, fishers and hunters.
Mr Phillips' family has since been appealing to the authorities to speed up the search.
His sister Sian Phillips spoke to the BBC from her Lancaster home, saying “every minute counts”.
She said: “We are really worried about him, and urge the authorities in Brazil to do all they can to search the route he was following. Time is crucial.
"We knew it was a dangerous place but Dom truly believed it was possible to safeguard the nature and the livelihoods of the indigenous people.
"He loves the country and cares deeply about the Amazon and the people there.”
Mr Phillips’ Brazilian wife, Alessandra Sampaio, also said: "Our families are in despair, please answer the urgency of the moment with urgent actions.
"Every second could be the difference between life and death.”
Mr Pereira's family has insisted that it is "essential that specialised searches are carried out, by air, river and land, with all the human and material resources that the situation requires."