What little is known about their donors suggests that the groups are emerging as a significant conduit for corporate spending on elections, allowing businesses to exercise political influence without fear of shareholder or customer reaction.

Democrats and government watchdog groups have urged the Internal Revenue Service to tighten oversight of these groups and to clarify the federal rules governing how much political activity is allowed without endangering their tax status. Agency officials said in July that they were considering revisions to the regulations, but gave no indication of what kind of changes they might make or when any changes might go into effect. In a letter sent to the I.R.S. on Monday, Senate Republicans warned the agency against changing the rules under political pressure.

Mr. Schneiderman, a Democrat elected in 2010, appears unwilling to wait. Under New York law, tax-exempt groups — including foundations, trade associations and social welfare organizations — that do business or raise substantial amounts of money in New York must file auditors’ reports and their federal tax returns with the attorney general’s office. With New York both the center of the country’s financial industry and home to many of its leading conservative and liberal donors, that jurisdiction could give Mr. Schneiderman oversight power over many of the biggest-spending groups.

“Given how many nonprofit organizations are raising tens or hundreds of millions of dollars and evading campaign finance disclosure laws, any and all scrutiny of these organizations by regulators is a welcome development,” said Paul S. Ryan, associate legal counsel of the Campaign Legal Center, which has pushed for tighter regulations.

The letters sent by Mr. Schneiderman’s office, part of a broader look into political activities by charitable organizations, went to groups that appear to fall under those regulations but have not filed the required paperwork, according to people with knowledge of the inquiry.