Israel confirmed the plans in a written statement to Al Jazeera.
In the statement, the housing ministry said the "52 housing units in Alkana substitute old housing units, which were built when the settlement was created 25 years ago".
"The 48 housing units in Ariel were approved by the ministry of defence many months ago, and they are inside an existing neighbourhood," the statement said.
The 2003 "road map", reaffirmed by Israeli and Palestinian leaders at a conference hosted by George Bush, the US president, in November last year, requires a halt to all settlement activity on occupied land where Palestinians seek statehood.
The new tenders were criticised by the Palestinian administration, led by Mahmoud Abbas, the Palestinian president.
"We condemn these plans and resolutions, which really undermine the peace process," said Saeb Erekat, the Palestinian negotiator, adding that Abbas would discuss the issue during talks with Bush next week.
Ehud Olmert, the Israeli prime minister, in keeping with the previous government's policy, has vowed to keep West Bank settlement blocs, including Ariel and Alkana, under any future peace accord.
The Olmert government argues that this warrants the continued building of homes within the settlement blocs, though US officials have consistently demanded a freeze.
"The current government never undertook not to build within settlement blocs," Zeev Boim, the Israeli housing minister said in a statement regarding tenders.
"Moreover, the current construction is intended to address internal needs of natural growth" in the settlements, he said.
Olmert is under pressure from nationalist members of his coalition government to keep up construction in West Bank settlements.
But Israel Radio reported that the Ariel and Alkana tenders could be challenged by the Labour party, Olmert's biggest coalition partner, over concerns that they would undermine talks with the Palestinians.