Eritrea has pulled troops back from its heavily militarised border with Ethiopia as a "gesture of reconciliation", the pro-government Eritrean Press agency said on its Facebook page.
There was no immediate confirmation from the government in Asmara, but the move would be consistent with rapidly improving ties between the Horn of Africa neighbours, whose 1998 war killed tens of thousands and led to two decades of military stalemate.
Ethiopia's Prime Minister Abiy Ahmed and Eritrea's President Isaias Afwerki signed an agreement in Asmara on July 9 to restore ties and have since taken steps to put it into practice including reopening embassies in each others countries.
"It is imperative for all those who care about the long-term stability and economic viability of the region to do everything they can to help the two countries move beyond the senseless war that wrought so much suffering on both peoples," the agency said.
Earlier on Thursday, Ethiopia appointed its first ambassador to Eritrea in two decades, the state-affiliated Fana news agency said. An online report from Fana said Redwan Hussien, formerly Ethiopian ambassador to Ireland, had become Addis Ababa's representative in Asmara.
Mr Abiy became prime minister in April and said he wanted to implement a peace deal that ended the war. The surprise decision was part of a broader effort to reform economics and politics in Ethiopia, the second-most populous country in Africa and east Africa's largest economy.
The reforms included releasing thousands of political prisoners, a big step in a tightly controlled country ruled by a coalition of parties that drove the previous regime from power in 1991.
Better relations between the two countries could eventually give landlocked Ethiopia access to Eritrea's ports and lay the groundwork for an easing of the political isolation of Eritrea.
Both leaders have visited each other, and Mr Isaias this week reopened his country's embassy in Addis Ababa.
Ethiopia's national carrier Ethiopia Airlines on Wednesday made its first flight to Asmara in two decades and was greeted by dancers waving flags and flowers as families separated for decades had emotional reunions.
Ethiopian Airlines is in talks to take a stake in Eritrean Airlines, Tewolde GebreMariam, chief executive of Ethiopian Airlines, said in an interview on Thursday, adding that a study would be conducted to determine the size of the stake.
In another sign of change, the new Ethiopian central bank governor met the business community and heads of major banks and listened to their complaints for two hours while private TV cameras rolled and journalists took notes.
"We are open to listen to the challenges of the business community unlike in previous days," said Yinager Dessie, who was appointed last month.
Business leaders said his predecessor was too conservative and sources in Addis Ababa said he rarely met bank executives and businesspeople and did not engage with institutions such as the World Bank and International Monetary Fund.
Mr Yinager pledged to meet the business community regularly and said two main concerns they raised, scant access to credit and crippling foreign exchange shortages, were government priorities.
"We are working on amending regulations and directives that have caused challenges for the business community," said Mr Yinager, who previously served as head of the government's National Planning Commission.
He also said that sweeping changes should be expected.
"It is inevitable to have a secondary market. We cannot be square and keep our economy closed to foreign markets," he said.
Ethiopian law currently does not allow any secondary markets. The state controls the banking sector and foreign banks are not allowed to invest in Ethiopian banks.
Yinager said Ethiopian banks should provide better services and said he told bank heads privately the average lending rate to 18 to 20 per cent is "not fair" to average people.
Ethiopia could sell stakes in state-owned firms as part of reforms to "unleash the potential of the private sector", the information minister told Reuters on Wednesday.