The bill, which will give the Senedd new powers, has been revised from its original draft amid worries it may reduce assembly powers.
But Mr Jones has expressed "considerable concern" that four months after the law's publication a number of issues have not been resolved.
The Wales Office said discussions would continue with the Welsh Government.
The Wales Bill has already been debated in the House of Commons and is now being considered by the House of Lords as part of the process of the law entering the statute book.
It will establish a new system for how the assembly makes laws, defining what is held back to Westminster in a list of reservations.
Ministers had revised the bill from a previous draft following criticism that it would reduce the assembly's powers, but AMs have warned that even the revised version threatens a roll-back in capabilities.
The committee stage of the proposed law's passage through the House of Lords is due to start on 31 October.
Ahead of the debate, the Lords Constitution Committee suggested the Wales Bill could create a "recipe for confusion" and could lead to more Welsh bills ending up in the courts.
AMs could refuse their permission for the Wales Bill to become law by voting against a legislative consent motion (LCM). The convention is not legally binding.
In a letter to Welsh Secretary Alun Cairns, Mr Jones wrote that "the UK government has publicly acknowledged" the bill can only proceed to royal assent if the assembly has resolved to give its legislative consent to the UK Parliament.
He said: "I will be looking to you to use your influence within the UK government to secure the necessary amendments so that the Welsh Government can commend the bill to the assembly.
"We are certainly not yet in that position, but I stand ready to discuss further with you as necessary."
Mr Jones said the issues included addressing those around a Welsh legal jurisdiction, and the number and breadth of reservations.
In particular, Mr Jones called for reservations on teachers' pay along with alcohol licensing, sale and supply to be removed from the bill.
"The judgement on whether to recommend that the assembly should give its legislative consent will inevitably be heavily influenced by the way the UK government deals with these matters at committee and report stages in the Lords," he said.
The Lords Constitution Committee said changes are needed to make sure the assembly's powers are not "inadvertently reduced".
Lord Lang, the chairman of the committee, said: "The list of reservations is so extensive, and the legal tests that govern the assembly's powers so complex and vague, that it could be a recipe for confusion and legal uncertainty.
"The outcome is likely to be increased litigation as the courts are asked to decide exactly where the boundaries of the assembly's authority lies."
A Wales Office spokesman said: "The Wales Bill provides a historic opportunity for the Welsh assembly to secure more powers and create a stronger, clearer fairer devolution settlement for Wales.
"Discussions will continue with the Welsh Government as the bill goes through Parliament and there will be plenty of opportunity to debate further amendments over the coming weeks."
The Welsh Government is not yet ready to commend the Wales Bill to AMs, First Minister Carwyn Jones has said.