Widodo declared an anti-drugs campaign soon after coming to power in 2014 and refused all requests for pardons from death-row drug convicts, ending a four-year moratorium.
But in recent months he has softened his position.
Asked in an interview with AFP on Monday whether he would consider a moratorium, Widodo said: "Why not? But I must ask my people.
"If my people say OK, they say yes, I will start to prepare," he said.
A moratorium could be the first step towards abolishing the death penalty, a move which needs approval in parliament which has been discussing the issue for the past year.
However, Widodo said it would be difficult to secure parliamentary backing without clear public support in a conservative, Muslim-majority country where voters are deeply concerned about high levels of addiction.
He cited a 2015 survey by a private pollster that found 85 percent of Indonesians support the death penalty for drug traffickers.
Since Widodo came to power, Indonesia has hauled 18 people -- 15 of them foreigners -- before the firing squad for drug trafficking.
They include a group of eight -- two Australians, a Brazilian, an Indonesian and four Nigerians -- who were put to death in a single night in April 2015 on the prison island of Nusakambangan.
The convicts were taken to a jungle clearing on the island, which houses several high-security prisons, and tied to stakes before being shot, in an move that triggered global revulsion.
The executions of Australian drug smugglers Andrew Chan and Myuran Sukumaran in particular caused tensions, with Indonesia's neighbour Australia temporarily recalling its ambassador from Jakarta.
Among the foreigners currently on death row are Frenchman Serge Atlaoui and Filipina Mary Jane Veloso, who were both pulled from the April 2015 round of executions.
A British grandmother, Lindsay Sandiford, is also on death row in Bali after she was caught smuggling a huge stash of cocaine into the resort island which attracts millions of visitors to its palm-fringed beaches every year.
Widodo has insisted that the death penalty is part of Indonesia's law and serves as deterrent against drug trafficking.
However, last November he said he was "open for options" to abolish it. In another concession, only drug convicts from countries that implement the death penalty were executed last year.
International and domestic rights groups have appealed to Indonesia to put a stop to capital punishment, arguing that miscarriages of justice are inevitable in a judicial system deeply compromised by corruption.
Ricky Gunawan from Community Legal Aid Foundation, a group calling for the abolition of the death penalty, said Widodo's latest comments were "a good sign that he is shifting from his stubbornness".
"But the downside is he leaves it to the people to decide, and a good leader should make a stance instead of leaving to the people to decide," he told AFP.
Gunawan urged President Francois Hollande, who will visit Indonesia this week, to press the issue during their talks. France scrapped the death penalty at a time when public support for it was high.
Some analysts have said that since Widodo is the first Indonesian president from outside the establishment -- he was not in the military nor part of the elites -- he needed to show a strong hand on law enforcement.
Halfway into his term, Widodo is faced with rising religious intolerance in a country that has always prided itself as a moderate Muslim nation.
In a case seen as a major test for pluralism, the governor of Jakarta -- an ethnic Chinese Christian - is currently on trial on allegations of blasphemy against Islam.
Widodo said that extensive freedoms have opened the way for hate speech, but played down the extent of intolerance, saying that a "small" number of incidents was "normal" in a nation that embraces many religions and ethnicities.
"People must know the balance of rights and duty... if they are too free, it is not good for our country," he said. "Indonesia is one of the most tolerant countries in the world."
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)